Detailed Description

template<typename Symmetry_>
class FermionBase< Symmetry_ >

This class provides the local operators for fermions in a SU(2)⊗U(1) block representation.

Definition at line 26 of file FermionBase.h.

#include <FermionBase.h>

Inheritance diagram for FermionBase< Symmetry_ >:

Public Types
typedef Symmetry_	Symmetry

typedef SiteOperatorQ< Symmetry, Eigen::Matrix< Scalar, Eigen::Dynamic, Eigen::Dynamic > >	OperatorType

typedef SiteOperatorQ< Symmetry, Eigen::Matrix< complex< Scalar >, Eigen::Dynamic, Eigen::Dynamic > >	ComplexOperatorType

typedef Symmetry::qType	qType

Public Member Functions
	FermionBase ()

	FermionBase (std::size_t L_input, bool REMOVE_DOUBLE=false, bool REMVOVE_EMPTY=false, bool REMOVE_UP=false, bool REMOVE_DN=false, int mfactor=1, int k_input=0)

Index	dim () const

std::size_t	orbitals () const

template<class Dummy = Symmetry>
std::enable_if<!Dummy::IS_SPIN_SU2(), SiteOperatorQ< Symmetry, Eigen::MatrixXcd > >::type	Rcomp (SPINOP_LABEL Sa, int orbital) const

OperatorType	Id (std::size_t orbital=0) const

ArrayXd	ZeroField () const

ArrayXXd	ZeroHopping () const

template<typename Scalar_ >
SiteOperatorQ< Symmetry_, Eigen::Matrix< Scalar_,-1,-1 > >	HubbardHamiltonian (const Array< Scalar_, Dynamic, 1 > &Uph, const Array< Scalar_, Dynamic, Dynamic > &t, const Array< Scalar_, Dynamic, Dynamic > &V, const Array< Scalar_, Dynamic, Dynamic > &J) const

template<typename Scalar_ , typename Dummy = Symmetry>
std::enable_if< Dummy::ABELIAN, SiteOperatorQ< Symmetry_, Eigen::Matrix< Scalar_,-1,-1 > > >::type	HubbardHamiltonian (const Array< Scalar_, Dynamic, 1 > &U, const Array< Scalar_, Dynamic, 1 > &Uph, const Array< Scalar_, Dynamic, 1 > &Eorb, const Array< Scalar_, Dynamic, 1 > &Bz, const Array< Scalar_, Dynamic, Dynamic > &t, const Array< Scalar_, Dynamic, Dynamic > &V, const Array< Scalar_, Dynamic, Dynamic > &Vz, const Array< Scalar_, Dynamic, Dynamic > &Vxy, const Array< Scalar_, Dynamic, Dynamic > &Jz, const Array< Scalar_, Dynamic, Dynamic > &Jxy, const Array< Scalar_, Dynamic, Dynamic > &C) const

template<typename Scalar_ , typename Dummy = Symmetry>
std::enable_if< Dummy::IS_SPIN_SU2() and!Dummy::IS_CHARGE_SU2(), SiteOperatorQ< Symmetry_, Eigen::Matrix< Scalar_,-1,-1 > > >::type	HubbardHamiltonian (const Array< Scalar_, Dynamic, 1 > &U, const Array< Scalar_, Dynamic, 1 > &Uph, const Array< Scalar_, Dynamic, 1 > &Eorb, const Array< Scalar_, Dynamic, Dynamic > &t, const Array< Scalar_, Dynamic, Dynamic > &V, const Array< Scalar_, Dynamic, Dynamic > &Vz, const Array< Scalar_, Dynamic, Dynamic > &Vxy, const Array< Scalar_, Dynamic, Dynamic > &J) const

template<typename Scalar_ , typename Dummy = Symmetry>
std::enable_if< Dummy::NO_SPIN_SYM() andDummy::IS_CHARGE_SU2(), SiteOperatorQ< Symmetry_, Eigen::Matrix< Scalar_,-1,-1 > > >::type	HubbardHamiltonian (const Array< Scalar_, Dynamic, 1 > &Uph, const Array< Scalar_, Dynamic, Dynamic > &t, const Array< Scalar_, Dynamic, Dynamic > &V, const Array< Scalar_, Dynamic, Dynamic > &Jz, const Array< Scalar_, Dynamic, Dynamic > &Jxy, const Array< Scalar_, Dynamic, 1 > &Bz, const Array< Scalar_, Dynamic, 1 > &Bx) const

template<typename Scalar_ , typename Dummy = Symmetry>
std::enable_if< Dummy::IS_SPIN_U1() andDummy::IS_CHARGE_SU2(), SiteOperatorQ< Symmetry_, Eigen::Matrix< Scalar_,-1,-1 > > >::type	HubbardHamiltonian (const Array< Scalar_, Dynamic, 1 > &Uph, const Array< Scalar_, Dynamic, Dynamic > &t, const Array< Scalar_, Dynamic, Dynamic > &V, const Array< Scalar_, Dynamic, Dynamic > &Jz, const Array< Scalar_, Dynamic, Dynamic > &Jxy, const Array< Scalar_, Dynamic, 1 > &Bz) const

template<typename Scalar_ , typename Dummy = Symmetry>
std::enable_if< Dummy::NO_SPIN_SYM(), SiteOperatorQ< Symmetry_, Eigen::Matrix< Scalar_,-1,-1 > > >::type	coupling_Bx (const Array< double, Dynamic, 1 > &Bx) const

template<typename Dummy = Symmetry>
std::enable_if< Dummy::NO_SPIN_SYM(), SiteOperatorQ< Symmetry_, Eigen::Matrix< complex< double >,-1,-1 > > >::type	coupling_By (const Array< double, Dynamic, 1 > &By) const

template<typename Scalar_ , typename Dummy = Symmetry>
std::enable_if< Dummy::IS_TRIVIAL, SiteOperatorQ< Symmetry_, Eigen::Matrix< Scalar_,-1,-1 > > >::type	coupling_singleFermion (const Array< double, Dynamic, 1 > &Fp) const

template<typename Scalar_ , typename Dummy = Symmetry>
std::enable_if< Dummy::NO_SPIN_SYM(), SiteOperatorQ< Symmetry_, Eigen::Matrix< Scalar_,-1,-1 > > >::type	coupling_XYZspin (const Array< double, Dynamic, Dynamic > &Jx, const Array< double, Dynamic, Dynamic > &Jy, const Array< double, Dynamic, Dynamic > &Jz) const

Qbasis< Symmetry >	get_basis () const

template<typename Dummy >
std::enable_if< Dummy::IS_SPIN_SU2() and!Dummy::IS_CHARGE_SU2(), SiteOperatorQ< Symmetry_, Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > > >::type	c (std::size_t orbital) const

template<typename Dummy >
std::enable_if< Dummy::IS_SPIN_SU2() and!Dummy::IS_CHARGE_SU2(), SiteOperatorQ< Symmetry_, Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > > >::type	cdag (std::size_t orbital) const

template<typename Dummy >
std::enable_if<!Dummy::IS_SPIN_SU2() and!Dummy::IS_CHARGE_SU2(), SiteOperatorQ< Symmetry_, Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > > >::type	c (SPIN_INDEX sigma, std::size_t orbital) const

template<typename Dummy >
std::enable_if<!Dummy::IS_SPIN_SU2() and!Dummy::IS_CHARGE_SU2(), SiteOperatorQ< Symmetry_, Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > > >::type	cdag (SPIN_INDEX sigma, std::size_t orbital) const

template<typename Dummy >
std::enable_if< Dummy::IS_CHARGE_SU2() and!Dummy::IS_SPIN_SU2(), SiteOperatorQ< Symmetry_, Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > > >::type	c (SPIN_INDEX sigma, SUB_LATTICE G, std::size_t orbital) const

template<typename Dummy >
std::enable_if< Dummy::IS_CHARGE_SU2() and!Dummy::IS_SPIN_SU2(), SiteOperatorQ< Symmetry_, Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > > >::type	cdag (SPIN_INDEX sigma, SUB_LATTICE G, std::size_t orbital) const

template<typename Dummy >
std::enable_if< Dummy::IS_CHARGE_SU2() andDummy::IS_SPIN_SU2(), SiteOperatorQ< Symmetry_, Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > > >::type	c (SUB_LATTICE G, std::size_t orbital) const

template<typename Dummy >
std::enable_if< Dummy::IS_CHARGE_SU2() andDummy::IS_SPIN_SU2(), SiteOperatorQ< Symmetry_, Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > > >::type	cdag (SUB_LATTICE G, std::size_t orbital) const

template<typename Dummy >
std::enable_if<!Dummy::IS_SPIN_SU2(), SiteOperatorQ< Symmetry_, Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > > >::type	n (SPIN_INDEX sigma, std::size_t orbital) const

template<typename Dummy >
std::enable_if< Dummy::IS_SPIN_SU2(), SiteOperatorQ< Symmetry_, Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > > >::type	S (std::size_t orbital) const

template<typename Dummy >
std::enable_if< Dummy::IS_SPIN_SU2(), SiteOperatorQ< Symmetry_, Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > > >::type	Sdag (std::size_t orbital) const

template<typename Dummy >
std::enable_if<!Dummy::IS_SPIN_SU2(), SiteOperatorQ< Symmetry_, Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > > >::type	Sz (std::size_t orbital) const

template<typename Dummy >
std::enable_if<!Dummy::IS_SPIN_SU2(), SiteOperatorQ< Symmetry_, Eigen::Matrix< complex< double >, Eigen::Dynamic, Eigen::Dynamic > > >::type	exp_ipiSz (std::size_t orbital) const

template<typename Dummy >
std::enable_if<!Dummy::IS_SPIN_SU2(), SiteOperatorQ< Symmetry_, Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > > >::type	Sp (std::size_t orbital) const

template<typename Dummy >
std::enable_if<!Dummy::IS_SPIN_SU2(), SiteOperatorQ< Symmetry_, Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > > >::type	Sm (std::size_t orbital) const

template<typename Dummy >
std::enable_if< Dummy::NO_SPIN_SYM(), SiteOperatorQ< Symmetry_, Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > > >::type	Sx (std::size_t orbital) const

template<typename Dummy >
std::enable_if< Dummy::NO_SPIN_SYM(), SiteOperatorQ< Symmetry_, Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > > >::type	iSy (std::size_t orbital) const

template<typename Dummy >
std::enable_if< Dummy::IS_CHARGE_SU2(), SiteOperatorQ< Symmetry_, Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > > >::type	T (std::size_t orbital) const

template<typename Dummy >
std::enable_if< Dummy::IS_CHARGE_SU2(), SiteOperatorQ< Symmetry_, Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > > >::type	Tdag (std::size_t orbital) const

template<typename Dummy >
std::enable_if<!Dummy::IS_CHARGE_SU2(), SiteOperatorQ< Symmetry_, Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > > >::type	cc (std::size_t orbital) const

template<typename Dummy >
std::enable_if<!Dummy::IS_CHARGE_SU2(), SiteOperatorQ< Symmetry_, Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > > >::type	cdagcdag (std::size_t orbital) const

template<typename Dummy >
std::enable_if<!Dummy::IS_CHARGE_SU2(), SiteOperatorQ< Symmetry_, Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > > >::type	Tz (std::size_t orbital) const

template<typename Dummy >
std::enable_if<!Dummy::IS_CHARGE_SU2(), SiteOperatorQ< Symmetry_, Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > > >::type	tz (std::size_t orbital) const

template<typename Dummy >
std::enable_if< Dummy::NO_CHARGE_SYM(), SiteOperatorQ< Symmetry_, Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > > >::type	Tx (std::size_t orbital, SUB_LATTICE G) const

template<typename Dummy >
std::enable_if< Dummy::NO_CHARGE_SYM(), SiteOperatorQ< Symmetry_, Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > > >::type	iTy (std::size_t orbital, SUB_LATTICE G) const

template<typename Scalar_ >
SiteOperatorQ< Symmetry_, Eigen::Matrix< Scalar_, Eigen::Dynamic, Eigen::Dynamic > >	HubbardHamiltonian (const Array< Scalar_, Dynamic, 1 > &Uph, const Array< Scalar_, Dynamic, Dynamic > &t, const Array< Scalar_, Dynamic, Dynamic > &V, const Array< Scalar_, Dynamic, Dynamic > &J) const


template<class Dummy = Symmetry>
std::enable_if< Dummy::IS_SPIN_SU2() and!Dummy::IS_CHARGE_SU2(), OperatorType >::type	c (size_t orbital=0) const

template<class Dummy = Symmetry>
std::enable_if<!Dummy::IS_SPIN_SU2() and!Dummy::IS_CHARGE_SU2(), OperatorType >::type	c (SPIN_INDEX sigma, size_t orbital=0) const

template<class Dummy = Symmetry>
std::enable_if< Dummy::IS_CHARGE_SU2() and!Dummy::IS_SPIN_SU2(), OperatorType >::type	c (SPIN_INDEX sigma, SUB_LATTICE G, size_t orbital=0) const

template<class Dummy = Symmetry>
std::enable_if< Dummy::IS_CHARGE_SU2() andDummy::IS_SPIN_SU2(), OperatorType >::type	c (SUB_LATTICE G, size_t orbital=0) const

template<class Dummy = Symmetry>
std::enable_if< Dummy::IS_SPIN_SU2() and!Dummy::IS_CHARGE_SU2(), OperatorType >::type	cdag (size_t orbital=0) const

template<class Dummy = Symmetry>
std::enable_if<!Dummy::IS_SPIN_SU2() and!Dummy::IS_CHARGE_SU2(), OperatorType >::type	cdag (SPIN_INDEX sigma, size_t orbital=0) const

template<class Dummy = Symmetry>
std::enable_if< Dummy::IS_CHARGE_SU2() and!Dummy::IS_SPIN_SU2(), OperatorType >::type	cdag (SPIN_INDEX sigma, SUB_LATTICE G, size_t orbital=0) const

template<class Dummy = Symmetry>
std::enable_if< Dummy::IS_CHARGE_SU2() andDummy::IS_SPIN_SU2(), OperatorType >::type	cdag (SUB_LATTICE G, size_t orbital=0) const

OperatorType	sign (std::size_t orb1=0, std::size_t orb2=0) const

OperatorType	sign_local (std::size_t orbital=0) const

template<class Dummy = Symmetry>
std::enable_if< true, OperatorType >::type	n (std::size_t orbital=0) const

template<class Dummy = Symmetry>
std::enable_if<!Dummy::IS_SPIN_SU2(), OperatorType >::type	n (SPIN_INDEX sigma, size_t orbital=0) const

template<class Dummy = Symmetry>
std::enable_if<!Dummy::IS_CHARGE_SU2(), OperatorType >::type	d (std::size_t orbital=0) const

OperatorType	ns (std::size_t orbital=0) const

OperatorType	nh (std::size_t orbital=0) const


template<class Dummy = Symmetry>
std::enable_if< Dummy::IS_SPIN_SU2(), OperatorType >::type	S (size_t orbital=0) const

template<class Dummy = Symmetry>
std::enable_if< Dummy::IS_SPIN_SU2(), OperatorType >::type	Sdag (size_t orbital=0) const

template<class Dummy = Symmetry>
std::enable_if<!Dummy::IS_SPIN_SU2(), OperatorType >::type	Sz (size_t orbital=0) const

template<class Dummy = Symmetry>
std::enable_if<!Dummy::IS_SPIN_SU2(), ComplexOperatorType >::type	exp_ipiSz (size_t orbital=0) const

template<class Dummy = Symmetry>
std::enable_if<!Dummy::IS_SPIN_SU2(), OperatorType >::type	Sp (size_t orbital=0) const

template<class Dummy = Symmetry>
std::enable_if<!Dummy::IS_SPIN_SU2(), OperatorType >::type	Sm (size_t orbital=0) const

template<class Dummy = Symmetry>
std::enable_if< Dummy::NO_SPIN_SYM(), OperatorType >::type	Sx (size_t orbital=0) const

template<class Dummy = Symmetry>
std::enable_if< Dummy::NO_SPIN_SYM(), OperatorType >::type	iSy (size_t orbital=0) const

template<class Dummy = Symmetry>
std::enable_if<!Dummy::IS_SPIN_SU2(), OperatorType >::type	Scomp (SPINOP_LABEL Sa, int orbital) const


template<class Dummy = Symmetry>
std::enable_if< Dummy::IS_CHARGE_SU2(), OperatorType >::type	T (size_t orbital=0) const

template<class Dummy = Symmetry>
std::enable_if< Dummy::IS_CHARGE_SU2(), OperatorType >::type	Tdag (size_t orbital=0) const

template<class Dummy = Symmetry>
std::enable_if<!Dummy::IS_CHARGE_SU2(), OperatorType >::type	Tz (size_t orbital=0) const

template<class Dummy = Symmetry>
std::enable_if<!Dummy::IS_CHARGE_SU2(), OperatorType >::type	tz (size_t orbital=0) const

template<class Dummy = Symmetry>
std::enable_if< Dummy::NO_CHARGE_SYM(), OperatorType >::type	Tx (size_t orbital=0, SUB_LATTICE G=A) const

template<class Dummy = Symmetry>
std::enable_if< Dummy::NO_CHARGE_SYM(), OperatorType >::type	iTy (size_t orbital=0, SUB_LATTICE G=A) const

template<class Dummy = Symmetry>
std::enable_if<!Dummy::IS_CHARGE_SU2(), OperatorType >::type	Tp (size_t orbital=0, SUB_LATTICE G=A) const

template<class Dummy = Symmetry>
std::enable_if<!Dummy::IS_CHARGE_SU2(), OperatorType >::type	Tm (size_t orbital=0, SUB_LATTICE G=A) const

template<class Dummy = Symmetry>
std::enable_if<!Dummy::IS_CHARGE_SU2(), OperatorType >::type	cc (size_t orbital=0) const

template<class Dummy = Symmetry>
std::enable_if<!Dummy::IS_CHARGE_SU2(), OperatorType >::type	cdagcdag (size_t orbital=0) const

Public Member Functions inherited from FermionSite< Symmetry_ >
	FermionSite ()

	FermionSite (bool REMOVE_DOUBLE, bool REMOVE_EMPTY, bool REMOVE_UP, bool REMOVE_DN, int mfactor_input=1, int k_input=0)

OperatorType	Id_1s () const

OperatorType	F_1s () const

OperatorType	c_1s (SPIN_INDEX sigma) const

OperatorType	cdag_1s (SPIN_INDEX sigma) const

OperatorType	n_1s () const

OperatorType	n_1s (SPIN_INDEX sigma) const

OperatorType	ns_1s () const

OperatorType	nh_1s () const

OperatorType	d_1s () const

OperatorType	Sz_1s () const

OperatorType	Sp_1s () const

OperatorType	Sm_1s () const

ComplexOperatorType	exp_ipiSz_1s () const

OperatorType	Tz_1s () const

OperatorType	cc_1s () const

OperatorType	cdagcdag_1s () const

Qbasis< Symmetry >	basis_1s () const

Private Types
typedef Eigen::Index	Index

typedef double	Scalar

Private Member Functions
OperatorType	make_operator (const OperatorType &Op_1s, size_t orbital=0, bool FERMIONIC=false, string label="") const

Private Attributes
std::size_t	N_orbitals

std::size_t	N_states

Qbasis< Symmetry >	TensorBasis

OperatorType	Id_vac

OperatorType	Zero_vac

Additional Inherited Members
Protected Member Functions inherited from FermionSite< Symmetry_ >
void	fill_basis (bool REMOVE_DOUBLE, bool REMOVE_EMPTY, bool REMOVE_UP, bool REMOVE_DN)

void	fill_SiteOps (bool REMOVE_DOUBLE, bool REMOVE_EMPTY, bool REMOVE_UP, bool REMOVE_DN)

Symmetry_::qType	getQ (SPIN_INDEX sigma, int Delta) const

Symmetry_::qType	getQ (SPINOP_LABEL Sa) const

Protected Attributes inherited from FermionSite< Symmetry_ >
int	mfactor = 1

int	k = 0

Qbasis< Symmetry >	basis_1s_

OperatorType	Id_1s_

OperatorType	F_1s_

OperatorType	cup_1s_

OperatorType	cdn_1s_

OperatorType	cdagup_1s_

OperatorType	cdagdn_1s_

OperatorType	n_1s_

OperatorType	nup_1s_

OperatorType	ndn_1s_

OperatorType	d_1s_

OperatorType	Sz_1s_

OperatorType	Sp_1s_

OperatorType	Sm_1s_

ComplexOperatorType	exp_ipiSz_1s_

OperatorType	Tz_1s_

OperatorType	cc_1s_

OperatorType	cdagcdag_1s_

Member Typedef Documentation

◆ ComplexOperatorType

template<typename Symmetry_ >

typedef SiteOperatorQ<Symmetry,Eigen::Matrix<complex<Scalar>,Eigen::Dynamic,Eigen::Dynamic> > FermionBase< Symmetry_ >::ComplexOperatorType

Definition at line 35 of file FermionBase.h.

◆ Index

template<typename Symmetry_ >

typedef Eigen::Index FermionBase< Symmetry_ >::Index

private

Definition at line 28 of file FermionBase.h.

◆ OperatorType

template<typename Symmetry_ >

typedef SiteOperatorQ<Symmetry,Eigen::Matrix<Scalar,Eigen::Dynamic,Eigen::Dynamic> > FermionBase< Symmetry_ >::OperatorType

Definition at line 34 of file FermionBase.h.

◆ qType

template<typename Symmetry_ >

typedef Symmetry::qType FermionBase< Symmetry_ >::qType

Definition at line 36 of file FermionBase.h.

◆ Scalar

template<typename Symmetry_ >

typedef double FermionBase< Symmetry_ >::Scalar

private

Definition at line 29 of file FermionBase.h.

◆ Symmetry

template<typename Symmetry_ >

typedef Symmetry_ FermionBase< Symmetry_ >::Symmetry

Definition at line 33 of file FermionBase.h.

Constructor & Destructor Documentation

◆ FermionBase() [1/2]

template<typename Symmetry_ >

FermionBase< Symmetry_ >::FermionBase ( )

inline

Definition at line 38 of file FermionBase.h.

◆ FermionBase() [2/2]

template<typename Symmetry_ >

FermionBase< Symmetry_ >::FermionBase	(	std::size_t	L_input,
		bool	REMOVE_DOUBLE = `false`,
		bool	REMVOVE_EMPTY = `false`,
		bool	REMOVE_UP = `false`,
		bool	REMOVE_DN = `false`,
		int	mfactor = `1`,
		int	k_input = `0`
	)

Parameters

L_input	: the amount of orbitals
U_IS_INFINITE	: if `true`, eliminates doubly-occupied sites from the basis

Definition at line 373 of file FermionBase.h.

Member Function Documentation

◆ c() [1/8]

template<typename Symmetry_ >

template<class Dummy = Symmetry>

std::enable_if< Dummy::IS_SPIN_SU2() and!Dummy::IS_CHARGE_SU2(), OperatorType >::type FermionBase< Symmetry_ >::c ( size_t orbital = 0 ) const

Annihilation operator

Parameters

orbital : orbital index

Note: The annihilation spinor is build as follows $c^{1/2} = \left( \begin{array}{c} -c_{\downarrow} \\ c_{\uparrow} \\ \end{array} \right)$ where the upper component corresponds to and the lower to .

◆ c() [2/8]

template<typename Symmetry_ >

template<class Dummy = Symmetry>

std::enable_if<!Dummy::IS_SPIN_SU2() and!Dummy::IS_CHARGE_SU2(), OperatorType >::type FermionBase< Symmetry_ >::c	(	SPIN_INDEX	sigma,
		size_t	orbital = `0`
	)		const

Annihilation operator

Parameters

orbital : orbital index

Note: The annihilation spinor is build as follows $c^{1/2} = \left( \begin{array}{c} -c_{\downarrow} \\ c_{\uparrow} \\ \end{array} \right)$ where the upper component corresponds to and the lower to .

◆ c() [3/8]

template<typename Symmetry_ >

template<typename Dummy >

std::enable_if<!Dummy::IS_SPIN_SU2() and!Dummy::IS_CHARGE_SU2(), SiteOperatorQ< Symmetry_, Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > > >::type FermionBase< Symmetry_ >::c	(	SPIN_INDEX	sigma,
		std::size_t	orbital
	)		const

Definition at line 453 of file FermionBase.h.

◆ c() [4/8]

template<typename Symmetry_ >

template<class Dummy = Symmetry>

std::enable_if< Dummy::IS_CHARGE_SU2() and!Dummy::IS_SPIN_SU2(), OperatorType >::type FermionBase< Symmetry_ >::c	(	SPIN_INDEX	sigma,
		SUB_LATTICE	G,
		size_t	orbital = `0`
	)		const

Annihilation operator

Parameters

orbital : orbital index

Note: The annihilation spinor is build as follows $c^{1/2} = \left( \begin{array}{c} -c_{\downarrow} \\ c_{\uparrow} \\ \end{array} \right)$ where the upper component corresponds to and the lower to .

◆ c() [5/8]

template<typename Symmetry_ >

template<typename Dummy >

std::enable_if< Dummy::IS_CHARGE_SU2() and!Dummy::IS_SPIN_SU2(), SiteOperatorQ< Symmetry_, Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > > >::type FermionBase< Symmetry_ >::c	(	SPIN_INDEX	sigma,
		SUB_LATTICE	G,
		std::size_t	orbital
	)		const

Definition at line 474 of file FermionBase.h.

◆ c() [6/8]

template<typename Symmetry_ >

template<typename Dummy >

std::enable_if< Dummy::IS_SPIN_SU2() and!Dummy::IS_CHARGE_SU2(), SiteOperatorQ< Symmetry_, Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > > >::type FermionBase< Symmetry_ >::c ( std::size_t orbital ) const

Definition at line 436 of file FermionBase.h.

◆ c() [7/8]

template<typename Symmetry_ >

template<class Dummy = Symmetry>

std::enable_if< Dummy::IS_CHARGE_SU2() andDummy::IS_SPIN_SU2(), OperatorType >::type FermionBase< Symmetry_ >::c	(	SUB_LATTICE	G,
		size_t	orbital = `0`
	)		const

Annihilation operator

Parameters

orbital : orbital index

Note: The annihilation spinor is build as follows $c^{1/2} = \left( \begin{array}{c} -c_{\downarrow} \\ c_{\uparrow} \\ \end{array} \right)$ where the upper component corresponds to and the lower to .

◆ c() [8/8]

template<typename Symmetry_ >

template<typename Dummy >

std::enable_if< Dummy::IS_CHARGE_SU2() andDummy::IS_SPIN_SU2(), SiteOperatorQ< Symmetry_, Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > > >::type FermionBase< Symmetry_ >::c	(	SUB_LATTICE	G,
		std::size_t	orbital
	)		const

Definition at line 495 of file FermionBase.h.

◆ cc() [1/2]

template<typename Symmetry_ >

template<class Dummy = Symmetry>

std::enable_if<!Dummy::IS_CHARGE_SU2(), OperatorType >::type FermionBase< Symmetry_ >::cc ( size_t orbital = 0 ) const

Orbital pairing η

Parameters

orbital : orbital index

◆ cc() [2/2]

template<typename Symmetry_ >

template<typename Dummy >

std::enable_if<!Dummy::IS_CHARGE_SU2(), SiteOperatorQ< Symmetry_, Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > > >::type FermionBase< Symmetry_ >::cc ( std::size_t orbital ) const

Definition at line 707 of file FermionBase.h.

◆ cdag() [1/8]

template<typename Symmetry_ >

template<class Dummy = Symmetry>

std::enable_if< Dummy::IS_SPIN_SU2() and!Dummy::IS_CHARGE_SU2(), OperatorType >::type FermionBase< Symmetry_ >::cdag ( size_t orbital = 0 ) const

Creation operator.

Parameters

orbital : orbital index

Note: The creation spinor is computed as $\left(c^{1/2}\right)^\dagger$ . The definition of cdag which is consistent with this computation is: $\left(c^{\dagger}\right)^{1/2} = \left( \begin{array}{c} c^\dagger_{\uparrow} \\ c^\dagger_{\downarrow} \\ \end{array} \right)$ where the upper component corresponds to and the lower to .

◆ cdag() [2/8]

template<typename Symmetry_ >

template<class Dummy = Symmetry>

std::enable_if<!Dummy::IS_SPIN_SU2() and!Dummy::IS_CHARGE_SU2(), OperatorType >::type FermionBase< Symmetry_ >::cdag	(	SPIN_INDEX	sigma,
		size_t	orbital = `0`
	)		const

Annihilation operator

Parameters

orbital : orbital index

Note: The annihilation spinor is build as follows $c^{1/2} = \left( \begin{array}{c} -c_{\downarrow} \\ c_{\uparrow} \\ \end{array} \right)$ where the upper component corresponds to and the lower to .

◆ cdag() [3/8]

template<typename Symmetry_ >

template<typename Dummy >

std::enable_if<!Dummy::IS_SPIN_SU2() and!Dummy::IS_CHARGE_SU2(), SiteOperatorQ< Symmetry_, Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > > >::type FermionBase< Symmetry_ >::cdag	(	SPIN_INDEX	sigma,
		std::size_t	orbital
	)		const

Definition at line 463 of file FermionBase.h.

◆ cdag() [4/8]

template<typename Symmetry_ >

template<class Dummy = Symmetry>

std::enable_if< Dummy::IS_CHARGE_SU2() and!Dummy::IS_SPIN_SU2(), OperatorType >::type FermionBase< Symmetry_ >::cdag	(	SPIN_INDEX	sigma,
		SUB_LATTICE	G,
		size_t	orbital = `0`
	)		const

Annihilation operator

Parameters

orbital : orbital index

Note: The annihilation spinor is build as follows $c^{1/2} = \left( \begin{array}{c} -c_{\downarrow} \\ c_{\uparrow} \\ \end{array} \right)$ where the upper component corresponds to and the lower to .

◆ cdag() [5/8]

template<typename Symmetry_ >

template<typename Dummy >

std::enable_if< Dummy::IS_CHARGE_SU2() and!Dummy::IS_SPIN_SU2(), SiteOperatorQ< Symmetry_, Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > > >::type FermionBase< Symmetry_ >::cdag	(	SPIN_INDEX	sigma,
		SUB_LATTICE	G,
		std::size_t	orbital
	)		const

Definition at line 484 of file FermionBase.h.

◆ cdag() [6/8]

template<typename Symmetry_ >

template<typename Dummy >

std::enable_if< Dummy::IS_SPIN_SU2() and!Dummy::IS_CHARGE_SU2(), SiteOperatorQ< Symmetry_, Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > > >::type FermionBase< Symmetry_ >::cdag ( std::size_t orbital ) const

Definition at line 444 of file FermionBase.h.

◆ cdag() [7/8]

template<typename Symmetry_ >

template<class Dummy = Symmetry>

std::enable_if< Dummy::IS_CHARGE_SU2() andDummy::IS_SPIN_SU2(), OperatorType >::type FermionBase< Symmetry_ >::cdag	(	SUB_LATTICE	G,
		size_t	orbital = `0`
	)		const

Annihilation operator

Parameters

orbital : orbital index

Note: The annihilation spinor is build as follows $c^{1/2} = \left( \begin{array}{c} -c_{\downarrow} \\ c_{\uparrow} \\ \end{array} \right)$ where the upper component corresponds to and the lower to .

◆ cdag() [8/8]

template<typename Symmetry_ >

template<typename Dummy >

std::enable_if< Dummy::IS_CHARGE_SU2() andDummy::IS_SPIN_SU2(), SiteOperatorQ< Symmetry_, Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > > >::type FermionBase< Symmetry_ >::cdag	(	SUB_LATTICE	G,
		std::size_t	orbital
	)		const

Definition at line 505 of file FermionBase.h.

◆ cdagcdag() [1/2]

template<typename Symmetry_ >

template<class Dummy = Symmetry>

std::enable_if<!Dummy::IS_CHARGE_SU2(), OperatorType >::type FermionBase< Symmetry_ >::cdagcdag ( size_t orbital = 0 ) const

Orbital paring η†

Parameters

orbital : orbital index

◆ cdagcdag() [2/2]

template<typename Symmetry_ >

template<typename Dummy >

std::enable_if<!Dummy::IS_CHARGE_SU2(), SiteOperatorQ< Symmetry_, Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > > >::type FermionBase< Symmetry_ >::cdagcdag ( std::size_t orbital ) const

Definition at line 715 of file FermionBase.h.

◆ coupling_Bx()

template<typename Symmetry_ >

template<typename Scalar_ , typename Dummy >

std::enable_if< Dummy::NO_SPIN_SYM(), SiteOperatorQ< Symmetry_, Eigen::Matrix< Scalar_,-1,-1 > > >::type FermionBase< Symmetry_ >::coupling_Bx ( const Array< double, Dynamic, 1 > & Bx ) const

Definition at line 1071 of file FermionBase.h.

◆ coupling_By()

template<typename Symmetry_ >

template<typename Dummy >

std::enable_if< Dummy::NO_SPIN_SYM(), SiteOperatorQ< Symmetry_, Eigen::Matrix< complex< double >,-1,-1 > > >::type FermionBase< Symmetry_ >::coupling_By ( const Array< double, Dynamic, 1 > & By ) const

Definition at line 1087 of file FermionBase.h.

◆ coupling_singleFermion()

template<typename Symmetry_ >

template<typename Scalar_ , typename Dummy >

std::enable_if< Dummy::IS_TRIVIAL, SiteOperatorQ< Symmetry_, Eigen::Matrix< Scalar_,-1,-1 > > >::type FermionBase< Symmetry_ >::coupling_singleFermion ( const Array< double, Dynamic, 1 > & Fp ) const

Definition at line 1103 of file FermionBase.h.

◆ coupling_XYZspin()

template<typename Symmetry_ >

template<typename Scalar_ , typename Dummy >

std::enable_if< Dummy::NO_SPIN_SYM(), SiteOperatorQ< Symmetry_, Eigen::Matrix< Scalar_,-1,-1 > > >::type FermionBase< Symmetry_ >::coupling_XYZspin	(	const Array< double, Dynamic, Dynamic > &	Jx,
		const Array< double, Dynamic, Dynamic > &	Jy,
		const Array< double, Dynamic, Dynamic > &	Jz
	)		const

Definition at line 1119 of file FermionBase.h.

◆ d()

template<typename Symmetry_ >

template<typename Dummy >

std::enable_if<!Dummy::IS_CHARGE_SU2(), SiteOperatorQ< Symmetry_, Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > > >::type FermionBase< Symmetry_ >::d ( std::size_t orbital = 0 ) const

Double occupation

Parameters

orbital : orbital index

Definition at line 578 of file FermionBase.h.

◆ dim()

template<typename Symmetry_ >

Index FermionBase< Symmetry_ >::dim ( ) const

inline

amount of states

Definition at line 47 of file FermionBase.h.

◆ exp_ipiSz() [1/2]

template<typename Symmetry_ >

template<class Dummy = Symmetry>

std::enable_if<!Dummy::IS_SPIN_SU2(), ComplexOperatorType >::type FermionBase< Symmetry_ >::exp_ipiSz ( size_t orbital = 0 ) const

Orbital spin

Parameters

orbital : orbital index

◆ exp_ipiSz() [2/2]

template<typename Symmetry_ >

template<typename Dummy >

std::enable_if<!Dummy::IS_SPIN_SU2(), SiteOperatorQ< Symmetry_, Eigen::Matrix< complex< double >, Eigen::Dynamic, Eigen::Dynamic > > >::type FermionBase< Symmetry_ >::exp_ipiSz ( std::size_t orbital ) const

Definition at line 636 of file FermionBase.h.

◆ get_basis()

template<typename Symmetry_ >

Qbasis< Symmetry > FermionBase< Symmetry_ >::get_basis ( ) const

inline

Returns the basis.

Definition at line 358 of file FermionBase.h.

◆ HubbardHamiltonian() [1/6]

template<typename Symmetry_ >

template<typename Scalar_ , typename Dummy >

std::enable_if< Dummy::ABELIAN, SiteOperatorQ< Symmetry_, Eigen::Matrix< Scalar_,-1,-1 > > >::type FermionBase< Symmetry_ >::HubbardHamiltonian	(	const Array< Scalar_, Dynamic, 1 > &	U,
		const Array< Scalar_, Dynamic, 1 > &	Uph,
		const Array< Scalar_, Dynamic, 1 > &	Eorb,
		const Array< Scalar_, Dynamic, 1 > &	Bz,
		const Array< Scalar_, Dynamic, Dynamic > &	t,
		const Array< Scalar_, Dynamic, Dynamic > &	V,
		const Array< Scalar_, Dynamic, Dynamic > &	Vz,
		const Array< Scalar_, Dynamic, Dynamic > &	Vxy,
		const Array< Scalar_, Dynamic, Dynamic > &	Jz,
		const Array< Scalar_, Dynamic, Dynamic > &	Jxy,
		const Array< Scalar_, Dynamic, Dynamic > &	C
	)		const

Definition at line 864 of file FermionBase.h.

◆ HubbardHamiltonian() [2/6]

template<typename Symmetry_ >

template<typename Scalar_ , typename Dummy >

std::enable_if< Dummy::IS_SPIN_SU2() and!Dummy::IS_CHARGE_SU2(), SiteOperatorQ< Symmetry_, Eigen::Matrix< Scalar_,-1,-1 > > >::type FermionBase< Symmetry_ >::HubbardHamiltonian	(	const Array< Scalar_, Dynamic, 1 > &	U,
		const Array< Scalar_, Dynamic, 1 > &	Uph,
		const Array< Scalar_, Dynamic, 1 > &	Eorb,
		const Array< Scalar_, Dynamic, Dynamic > &	t,
		const Array< Scalar_, Dynamic, Dynamic > &	V,
		const Array< Scalar_, Dynamic, Dynamic > &	Vz,
		const Array< Scalar_, Dynamic, Dynamic > &	Vxy,
		const Array< Scalar_, Dynamic, Dynamic > &	J
	)		const

Definition at line 939 of file FermionBase.h.

◆ HubbardHamiltonian() [3/6]

template<typename Symmetry_ >

template<typename Scalar_ >

SiteOperatorQ< Symmetry_, Eigen::Matrix< Scalar_,-1,-1 > > FermionBase< Symmetry_ >::HubbardHamiltonian	(	const Array< Scalar_, Dynamic, 1 > &	Uph,
		const Array< Scalar_, Dynamic, Dynamic > &	t,
		const Array< Scalar_, Dynamic, Dynamic > &	V,
		const Array< Scalar_, Dynamic, Dynamic > &	J
	)		const

Creates the full Hubbard Hamiltonian on the supersite with orbital-dependent U.

Parameters

U	: for each orbital
Uph	: particle-hole symmetric for each orbital (times $(n_{\uparrow}-1/2)(n_{\downarrow}-1/2)+1/4$ )
Eorb	: $\varepsilon$ onsite energy for each orbital
t	:
V	:
Vz	:
Vxy	: $V_{xy}$
J	:

◆ HubbardHamiltonian() [4/6]

template<typename Symmetry_ >

template<typename Scalar_ >

SiteOperatorQ< Symmetry_, Eigen::Matrix< Scalar_, Eigen::Dynamic, Eigen::Dynamic > > FermionBase< Symmetry_ >::HubbardHamiltonian	(	const Array< Scalar_, Dynamic, 1 > &	Uph,
		const Array< Scalar_, Dynamic, Dynamic > &	t,
		const Array< Scalar_, Dynamic, Dynamic > &	V,
		const Array< Scalar_, Dynamic, Dynamic > &	J
	)		const

Definition at line 783 of file FermionBase.h.

◆ HubbardHamiltonian() [5/6]

template<typename Symmetry_ >

template<typename Scalar_ , typename Dummy >

std::enable_if< Dummy::IS_SPIN_U1() andDummy::IS_CHARGE_SU2(), SiteOperatorQ< Symmetry_, Eigen::Matrix< Scalar_,-1,-1 > > >::type FermionBase< Symmetry_ >::HubbardHamiltonian	(	const Array< Scalar_, Dynamic, 1 > &	Uph,
		const Array< Scalar_, Dynamic, Dynamic > &	t,
		const Array< Scalar_, Dynamic, Dynamic > &	V,
		const Array< Scalar_, Dynamic, Dynamic > &	Jz,
		const Array< Scalar_, Dynamic, Dynamic > &	Jxy,
		const Array< Scalar_, Dynamic, 1 > &	Bz
	)		const

Definition at line 1033 of file FermionBase.h.

◆ HubbardHamiltonian() [6/6]

template<typename Symmetry_ >

template<typename Scalar_ , typename Dummy >

std::enable_if< Dummy::NO_SPIN_SYM() andDummy::IS_CHARGE_SU2(), SiteOperatorQ< Symmetry_, Eigen::Matrix< Scalar_,-1,-1 > > >::type FermionBase< Symmetry_ >::HubbardHamiltonian	(	const Array< Scalar_, Dynamic, 1 > &	Uph,
		const Array< Scalar_, Dynamic, Dynamic > &	t,
		const Array< Scalar_, Dynamic, Dynamic > &	V,
		const Array< Scalar_, Dynamic, Dynamic > &	Jz,
		const Array< Scalar_, Dynamic, Dynamic > &	Jxy,
		const Array< Scalar_, Dynamic, 1 > &	Bz,
		const Array< Scalar_, Dynamic, 1 > &	Bx
	)		const

Definition at line 990 of file FermionBase.h.

◆ Id()

template<typename Symmetry_ >

SiteOperatorQ< Symmetry_, Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > > FermionBase< Symmetry_ >::Id ( std::size_t orbital = 0 ) const

Identity

Definition at line 775 of file FermionBase.h.

◆ iSy() [1/2]

template<typename Symmetry_ >

template<class Dummy = Symmetry>

std::enable_if< Dummy::NO_SPIN_SYM(), OperatorType >::type FermionBase< Symmetry_ >::iSy ( size_t orbital = 0 ) const

Orbital spin

Parameters

orbital : orbital index

◆ iSy() [2/2]

template<typename Symmetry_ >

template<typename Dummy >

std::enable_if< Dummy::NO_SPIN_SYM(), SiteOperatorQ< Symmetry_, Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > > >::type FermionBase< Symmetry_ >::iSy ( std::size_t orbital ) const

Definition at line 681 of file FermionBase.h.

◆ iTy() [1/2]

template<typename Symmetry_ >

template<class Dummy = Symmetry>

std::enable_if< Dummy::NO_CHARGE_SYM(), OperatorType >::type FermionBase< Symmetry_ >::iTy	(	size_t	orbital = `0`,
		SUB_LATTICE	G = `A`
	)		const

Isospin y-component

Parameters

orbital : orbital index

◆ iTy() [2/2]

template<typename Symmetry_ >

template<typename Dummy >

std::enable_if< Dummy::NO_CHARGE_SYM(), SiteOperatorQ< Symmetry_, Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > > >::type FermionBase< Symmetry_ >::iTy	(	std::size_t	orbital,
		SUB_LATTICE	G
	)		const

Definition at line 766 of file FermionBase.h.

◆ make_operator()

template<typename Symmetry_ >

SiteOperatorQ< Symmetry_, Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > > FermionBase< Symmetry_ >::make_operator	(	const OperatorType &	Op_1s,
		size_t	orbital = `0`,
		bool	FERMIONIC = `false`,
		string	label = `""`
	)		const

private

Definition at line 405 of file FermionBase.h.

◆ n() [1/3]

template<typename Symmetry_ >

template<class Dummy = Symmetry>

std::enable_if<!Dummy::IS_SPIN_SU2(), OperatorType >::type FermionBase< Symmetry_ >::n	(	SPIN_INDEX	sigma,
		size_t	orbital = `0`
	)		const

Annihilation operator

Parameters

orbital : orbital index

Note: The annihilation spinor is build as follows $c^{1/2} = \left( \begin{array}{c} -c_{\downarrow} \\ c_{\uparrow} \\ \end{array} \right)$ where the upper component corresponds to and the lower to .

◆ n() [2/3]

template<typename Symmetry_ >

template<typename Dummy >

std::enable_if<!Dummy::IS_SPIN_SU2(), SiteOperatorQ< Symmetry_, Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > > >::type FermionBase< Symmetry_ >::n	(	SPIN_INDEX	sigma,
		std::size_t	orbital
	)		const

Definition at line 554 of file FermionBase.h.

◆ n() [3/3]

template<typename Symmetry_ >

template<typename Dummy >

std::enable_if< true, SiteOperatorQ< Symmetry_, Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > > >::type FermionBase< Symmetry_ >::n ( std::size_t orbital = 0 ) const

Occupation number operator

Parameters

orbital : orbital index

Definition at line 546 of file FermionBase.h.

◆ nh()

template<typename Symmetry_ >

SiteOperatorQ< Symmetry_, Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > > FermionBase< Symmetry_ >::nh ( std::size_t orbital = 0 ) const

Holon density $n_h=2d-n-1=1-n_s$

Parameters

orbital : orbital index

Definition at line 570 of file FermionBase.h.

◆ ns()

template<typename Symmetry_ >

SiteOperatorQ< Symmetry_, Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > > FermionBase< Symmetry_ >::ns ( std::size_t orbital = 0 ) const

Spinon density $n_s=n-2d$

Parameters

orbital : orbital index

Definition at line 563 of file FermionBase.h.

◆ orbitals()

template<typename Symmetry_ >

std::size_t FermionBase< Symmetry_ >::orbitals ( ) const

inline

amount of orbitals

Definition at line 50 of file FermionBase.h.

◆ Rcomp()

template<typename Symmetry_ >

template<typename Dummy >

std::enable_if<!Dummy::IS_SPIN_SU2(), SiteOperatorQ< Symmetry_, Eigen::Matrix< complex< double >, Eigen::Dynamic, Eigen::Dynamic > > >::type FermionBase< Symmetry_ >::Rcomp	(	SPINOP_LABEL	Sa,
		int	orbital
	)		const

Definition at line 586 of file FermionBase.h.

◆ S() [1/2]

template<typename Symmetry_ >

template<class Dummy = Symmetry>

std::enable_if< Dummy::IS_SPIN_SU2(), OperatorType >::type FermionBase< Symmetry_ >::S ( size_t orbital = 0 ) const

Orbital spin

Parameters

orbital : orbital index

◆ S() [2/2]

template<typename Symmetry_ >

template<typename Dummy >

std::enable_if< Dummy::IS_SPIN_SU2(), SiteOperatorQ< Symmetry_, Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > > >::type FermionBase< Symmetry_ >::S ( std::size_t orbital ) const

Definition at line 612 of file FermionBase.h.

◆ Scomp()

template<typename Symmetry_ >

template<class Dummy = Symmetry>

std::enable_if<!Dummy::IS_SPIN_SU2(), OperatorType >::type FermionBase< Symmetry_ >::Scomp	(	SPINOP_LABEL	Sa,
		int	orbital
	)		const

inline

Orbital spin

Parameters

orbital : orbital index

Definition at line 179 of file FermionBase.h.

◆ Sdag() [1/2]

template<typename Symmetry_ >

template<class Dummy = Symmetry>

std::enable_if< Dummy::IS_SPIN_SU2(), OperatorType >::type FermionBase< Symmetry_ >::Sdag ( size_t orbital = 0 ) const

Orbital spin†

Parameters

orbital : orbital index

◆ Sdag() [2/2]

template<typename Symmetry_ >

template<typename Dummy >

std::enable_if< Dummy::IS_SPIN_SU2(), SiteOperatorQ< Symmetry_, Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > > >::type FermionBase< Symmetry_ >::Sdag ( std::size_t orbital ) const

Definition at line 620 of file FermionBase.h.

◆ sign()

template<typename Symmetry_ >

SiteOperatorQ< Symmetry_, Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > > FermionBase< Symmetry_ >::sign	(	std::size_t	orb1 = `0`,
		std::size_t	orb2 = `0`
	)		const

Fermionic sign for the hopping between two orbitals of nearest-neighbour supersites of a ladder.

Parameters

orb1	: orbital on supersite i
orb2	: orbital on supersite i+1

Definition at line 522 of file FermionBase.h.

◆ sign_local()

template<typename Symmetry_ >

SiteOperatorQ< Symmetry_, Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > > FermionBase< Symmetry_ >::sign_local ( std::size_t orbital = 0 ) const

Fermionic sign for one orbital of a supersite.

Parameters

orbital : orbital index

Definition at line 515 of file FermionBase.h.

◆ Sm() [1/2]

template<typename Symmetry_ >

template<class Dummy = Symmetry>

std::enable_if<!Dummy::IS_SPIN_SU2(), OperatorType >::type FermionBase< Symmetry_ >::Sm ( size_t orbital = 0 ) const

Orbital spin

Parameters

orbital : orbital index

◆ Sm() [2/2]

template<typename Symmetry_ >

template<typename Dummy >

std::enable_if<!Dummy::IS_SPIN_SU2(), SiteOperatorQ< Symmetry_, Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > > >::type FermionBase< Symmetry_ >::Sm ( std::size_t orbital ) const

Definition at line 663 of file FermionBase.h.

◆ Sp() [1/2]

template<typename Symmetry_ >

template<class Dummy = Symmetry>

std::enable_if<!Dummy::IS_SPIN_SU2(), OperatorType >::type FermionBase< Symmetry_ >::Sp ( size_t orbital = 0 ) const

Orbital spin

Parameters

orbital : orbital index

◆ Sp() [2/2]

template<typename Symmetry_ >

template<typename Dummy >

std::enable_if<!Dummy::IS_SPIN_SU2(), SiteOperatorQ< Symmetry_, Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > > >::type FermionBase< Symmetry_ >::Sp ( std::size_t orbital ) const

Definition at line 655 of file FermionBase.h.

◆ Sx() [1/2]

template<typename Symmetry_ >

template<class Dummy = Symmetry>

std::enable_if< Dummy::NO_SPIN_SYM(), OperatorType >::type FermionBase< Symmetry_ >::Sx ( size_t orbital = 0 ) const

Orbital spin

Parameters

orbital : orbital index

◆ Sx() [2/2]

template<typename Symmetry_ >

template<typename Dummy >

std::enable_if< Dummy::NO_SPIN_SYM(), SiteOperatorQ< Symmetry_, Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > > >::type FermionBase< Symmetry_ >::Sx ( std::size_t orbital ) const

Definition at line 671 of file FermionBase.h.

◆ Sz() [1/2]

template<typename Symmetry_ >

template<class Dummy = Symmetry>

std::enable_if<!Dummy::IS_SPIN_SU2(), OperatorType >::type FermionBase< Symmetry_ >::Sz ( size_t orbital = 0 ) const

Orbital spin

Parameters

orbital : orbital index

◆ Sz() [2/2]

template<typename Symmetry_ >

template<typename Dummy >

std::enable_if<!Dummy::IS_SPIN_SU2(), SiteOperatorQ< Symmetry_, Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > > >::type FermionBase< Symmetry_ >::Sz ( std::size_t orbital ) const

Definition at line 628 of file FermionBase.h.

◆ T() [1/2]

template<typename Symmetry_ >

template<class Dummy = Symmetry>

std::enable_if< Dummy::IS_CHARGE_SU2(), OperatorType >::type FermionBase< Symmetry_ >::T ( size_t orbital = 0 ) const

Orbital Isospin

Parameters

orbital : orbital index

◆ T() [2/2]

template<typename Symmetry_ >

template<typename Dummy >

std::enable_if< Dummy::IS_CHARGE_SU2(), SiteOperatorQ< Symmetry_, Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > > >::type FermionBase< Symmetry_ >::T ( std::size_t orbital ) const

Definition at line 691 of file FermionBase.h.

◆ Tdag() [1/2]

template<typename Symmetry_ >

template<class Dummy = Symmetry>

std::enable_if< Dummy::IS_CHARGE_SU2(), OperatorType >::type FermionBase< Symmetry_ >::Tdag ( size_t orbital = 0 ) const

Orbital Isospin†

Parameters

orbital : orbital index

◆ Tdag() [2/2]

template<typename Symmetry_ >

template<typename Dummy >

std::enable_if< Dummy::IS_CHARGE_SU2(), SiteOperatorQ< Symmetry_, Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > > >::type FermionBase< Symmetry_ >::Tdag ( std::size_t orbital ) const

Definition at line 699 of file FermionBase.h.

◆ Tm()

template<typename Symmetry_ >

template<class Dummy = Symmetry>

std::enable_if<!Dummy::IS_CHARGE_SU2(), OperatorType >::type FermionBase< Symmetry_ >::Tm	(	size_t	orbital = `0`,
		SUB_LATTICE	G = `A`
	)		const

inline

Orbital Isospin

Parameters

orbital : orbital index

Definition at line 251 of file FermionBase.h.

◆ Tp()

template<typename Symmetry_ >

template<class Dummy = Symmetry>

std::enable_if<!Dummy::IS_CHARGE_SU2(), OperatorType >::type FermionBase< Symmetry_ >::Tp	(	size_t	orbital = `0`,
		SUB_LATTICE	G = `A`
	)		const

inline

Orbital Isospin

Parameters

orbital : orbital index

Definition at line 244 of file FermionBase.h.

◆ Tx() [1/2]

template<typename Symmetry_ >

template<class Dummy = Symmetry>

std::enable_if< Dummy::NO_CHARGE_SYM(), OperatorType >::type FermionBase< Symmetry_ >::Tx	(	size_t	orbital = `0`,
		SUB_LATTICE	G = `A`
	)		const

Isospin x-component

Parameters

orbital : orbital index

◆ Tx() [2/2]

template<typename Symmetry_ >

template<typename Dummy >

std::enable_if< Dummy::NO_CHARGE_SYM(), SiteOperatorQ< Symmetry_, Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > > >::type FermionBase< Symmetry_ >::Tx	(	std::size_t	orbital,
		SUB_LATTICE	G
	)		const

Definition at line 756 of file FermionBase.h.

◆ Tz() [1/2]

template<typename Symmetry_ >

template<class Dummy = Symmetry>

std::enable_if<!Dummy::IS_CHARGE_SU2(), OperatorType >::type FermionBase< Symmetry_ >::Tz ( size_t orbital = 0 ) const

Isospin z-component

Parameters

orbital : orbital index

◆ tz() [1/2]

template<typename Symmetry_ >

template<class Dummy = Symmetry>

std::enable_if<!Dummy::IS_CHARGE_SU2(), OperatorType >::type FermionBase< Symmetry_ >::tz ( size_t orbital = 0 ) const

Orbital Isospin

Parameters

orbital : orbital index

◆ Tz() [2/2]

template<typename Symmetry_ >

template<typename Dummy >

std::enable_if<!Dummy::IS_CHARGE_SU2(), SiteOperatorQ< Symmetry_, Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > > >::type FermionBase< Symmetry_ >::Tz ( std::size_t orbital ) const

Definition at line 736 of file FermionBase.h.

◆ tz() [2/2]

template<typename Symmetry_ >

template<typename Dummy >

std::enable_if<!Dummy::IS_CHARGE_SU2(), SiteOperatorQ< Symmetry_, Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > > >::type FermionBase< Symmetry_ >::tz ( std::size_t orbital ) const

Definition at line 746 of file FermionBase.h.

◆ ZeroField()

template<typename Symmetry_ >

ArrayXd FermionBase< Symmetry_ >::ZeroField ( ) const

inline

Returns an array of size dim() with zeros.

Definition at line 277 of file FermionBase.h.

◆ ZeroHopping()

template<typename Symmetry_ >

ArrayXXd FermionBase< Symmetry_ >::ZeroHopping ( ) const

inline

Returns an array of size dim()xdim() with zeros.

Definition at line 280 of file FermionBase.h.

Member Data Documentation

◆ Id_vac

template<typename Symmetry_ >

OperatorType FermionBase< Symmetry_ >::Id_vac

private

Definition at line 369 of file FermionBase.h.

◆ N_orbitals

template<typename Symmetry_ >

std::size_t FermionBase< Symmetry_ >::N_orbitals

private

Definition at line 363 of file FermionBase.h.

◆ N_states

template<typename Symmetry_ >

std::size_t FermionBase< Symmetry_ >::N_states

private

Definition at line 364 of file FermionBase.h.

◆ TensorBasis

template<typename Symmetry_ >

Qbasis<Symmetry> FermionBase< Symmetry_ >::TensorBasis

private

Definition at line 366 of file FermionBase.h.

◆ Zero_vac

template<typename Symmetry_ >

OperatorType FermionBase< Symmetry_ >::Zero_vac

private

Definition at line 369 of file FermionBase.h.

The documentation for this class was generated from the following file:

FermionBase.h

Detailed Description

Public Types

Public Member Functions

Private Types

Private Member Functions

Private Attributes

Additional Inherited Members

Member Typedef Documentation

◆ ComplexOperatorType

◆ Index

◆ OperatorType

◆ qType

◆ Scalar

◆ Symmetry

Constructor & Destructor Documentation

◆ FermionBase() [1/2]

◆ FermionBase() [2/2]

Member Function Documentation

◆ c() [1/8]

◆ c() [2/8]

◆ c() [3/8]

◆ c() [4/8]

◆ c() [5/8]

◆ c() [6/8]

◆ c() [7/8]

◆ c() [8/8]

◆ cc() [1/2]

◆ cc() [2/2]

◆ cdag() [1/8]

◆ cdag() [2/8]

◆ cdag() [3/8]

◆ cdag() [4/8]

◆ cdag() [5/8]

◆ cdag() [6/8]

◆ cdag() [7/8]

◆ cdag() [8/8]

◆ cdagcdag() [1/2]

◆ cdagcdag() [2/2]

◆ coupling_Bx()

◆ coupling_By()

◆ coupling_singleFermion()

◆ coupling_XYZspin()

◆ d()

◆ dim()

◆ exp_ipiSz() [1/2]

◆ exp_ipiSz() [2/2]

◆ get_basis()

◆ HubbardHamiltonian() [1/6]

◆ HubbardHamiltonian() [2/6]

◆ HubbardHamiltonian() [3/6]

◆ HubbardHamiltonian() [4/6]

◆ HubbardHamiltonian() [5/6]

◆ HubbardHamiltonian() [6/6]

◆ Id()

◆ iSy() [1/2]

◆ iSy() [2/2]

◆ iTy() [1/2]

◆ iTy() [2/2]

◆ make_operator()

◆ n() [1/3]

◆ n() [2/3]

◆ n() [3/3]

◆ nh()

◆ ns()

◆ orbitals()

◆ Rcomp()

◆ S() [1/2]

◆ S() [2/2]

◆ Scomp()

◆ Sdag() [1/2]

◆ Sdag() [2/2]

◆ sign()

◆ sign_local()

◆ Sm() [1/2]

◆ Sm() [2/2]

◆ Sp() [1/2]

◆ Sp() [2/2]

◆ Sx() [1/2]

◆ Sx() [2/2]

◆ Sz() [1/2]