Detailed Description

MPO representation of

$H = -t \sum_{<ij>} \left(c^\dagger_i c_j + h.c.\right) +\Delta \sum_{<ij>} \left(c^\dagger_i c_j + h.c.\right) -\mu \sum_i n_i$

Note: Internally, a Heisenberg model is used with the following relations: , $S^-=c^{\dagger}$ , ,; Uses the Z(2) symmetry, corresponding to the parity of the fermions (odd or even).; The default variable settings can be seen in SpinlessFermionsZ2::defaults.

Definition at line 26 of file SpinlessFermionsZ2.h.

#include <SpinlessFermionsZ2.h>

Inheritance diagram for VMPS::SpinlessFermionsZ2:

[legend]

Public Types
typedef Sym::ZN< Sym::ChargeZ2, 2 >	Symmetry

Public Types inherited from Mpo< Sym::ZN< Sym::ChargeZ2, 2 > >
typedef SparseMatrixXd	SparseMatrixType

typedef SiteOperator< Sym::ZN< Sym::ChargeZ2, 2 >, double >	OperatorType

typedef Symmetry::qType	qType

typedef Matrix< double, Dynamic, Dynamic >	MatrixType

typedef double	Scalar_

typedef Mps< Sym::ZN< Sym::ChargeZ2, 2 >, double >	StateXd

typedef Umps< Sym::ZN< Sym::ChargeZ2, 2 >, double >	StateUd

typedef Mps< Sym::ZN< Sym::ChargeZ2, 2 >, std::complex< double > >	StateXcd

typedef Umps< Sym::ZN< Sym::ChargeZ2, 2 >, std::complex< double > >	StateUcd

typedef MpsCompressor< Sym::ZN< Sym::ChargeZ2, 2 >, double, double >	CompressorXd

typedef MpsCompressor< Sym::ZN< Sym::ChargeZ2, 2 >, std::complex< double >, double >	CompressorXcd

typedef Mpo< Sym::ZN< Sym::ChargeZ2, 2 > >	Operator

Public Types inherited from MpoTerms< Symmetry, Scalar >
typedef SiteOperator< Symmetry, Scalar >	OperatorType

typedef Symmetry::qType	qType

typedef Eigen::SparseMatrix< Scalar, Eigen::ColMajor, EIGEN_DEFAULT_SPARSE_INDEX_TYPE >	MatrixType

Public Member Functions

	SpinlessFermionsZ2 ()

	SpinlessFermionsZ2 (const size_t &L, const vector< Param > &params)

Public Member Functions inherited from Mpo< Sym::ZN< Sym::ChargeZ2, 2 > >
	Mpo ()

	Mpo (MpoTerms< Sym::ZN< Sym::ChargeZ2, 2 >, double > &Terms)

	Mpo (size_t L_input)

	Mpo (std::size_t L_input, qType Qtot_input, std::string label_input="Mpo", bool HERMITIAN_input=false, bool UNITARY_input=false, BC BC_input=BC::OPEN, DMRG::VERBOSITY::OPTION VERB_input=DMRG::VERBOSITY::OPTION::SILENT)

void	construct_from_pushlist (const PushType< OperatorType, CouplScalar > &pushlist, const std::vector< std::vector< std::string > > &labellist, size_t Lcell)

void	calc_reversedData_from_pushlist (const PushType< OperatorType, CouplScalar > &pushlist, double tolerance=::mynumeric_limits< double >::epsilon())

void	push_qpath (const std::size_t loc, const std::vector< OperatorType > &opList, const std::vector< qType > &qList, const double lambda=1.0)

void	setLocal (std::size_t loc, const OperatorType &op)

void	setLocal (std::size_t loc, const OperatorType &op, const OperatorType &signOp)

void	setLocal (std::size_t loc, const OperatorType &op, const std::vector< OperatorType > &signOp)

void	setLocal (const std::vector< std::size_t > &locs, const std::vector< OperatorType > &ops)

void	setLocal (const std::vector< std::size_t > &locs, const std::vector< OperatorType > &ops, const OperatorType &signOp)

void	setLocal (const std::vector< std::size_t > &locs, const std::vector< OperatorType > &ops, const std::vector< OperatorType > &signOps)

void	setLocalStag (std::size_t loc, const OperatorType &op, const std::vector< OperatorType > &stagSignOps)

void	setLocalSum (const OperatorType &op, double(*f)(int)=localSumTrivial)

void	setLocalSum (const std::vector< OperatorType > &op, std::vector< double > coeffs)

void	setProductSum (const OperatorType &op1, const OperatorType &op2)

void	precalc_TwoSiteData (bool FORCE=false)

std::string	info (bool REDUCED=false) const

int	get_dAux_max (int power=1) const

std::size_t	length () const

std::size_t	volume () const

int	locality () const

void	set_locality (std::size_t LocalSite_input)

OperatorType	localOperator () const

void	set_localOperator (OperatorType LocalOp_input)

Mpo< Sym::ZN< Sym::ChargeZ2, 2 >, double >	Identity () const

Mpo< Sym::ZN< Sym::ChargeZ2, 2 >, double >	Zero () const

bool	IS_UNITARY () const

bool	IS_HERMITIAN () const

bool	IS_HAMILTONIAN () const

bool	HAS_TWO_SITE_DATA () const

bool	HAS_W () const

boost::multi_array< double, 4 >	H2site (std::size_t loc, bool HALF_THE_LOCAL_TERM=false) const

void	generate_label (std::size_t Lcell)

void	push_width (const std::size_t n, const std::size_t loc, const double lambda, const OperatorType &outOp, const std::vector< OperatorType > &trans, const OperatorType &inOp)

void	push_local (const std::size_t loc, const double lambda, const OperatorType &op)

void	push_tight (const std::size_t loc, const double lambda, const OperatorType &op1, const OperatorType &op2)

void	push_nextn (const std::size_t loc, const double lambda, const OperatorType &op1, const OperatorType &trans, const OperatorType &op2)

Public Member Functions inherited from MpoTerms< Symmetry, Scalar >
void	reconstruct (const std::vector< std::map< std::array< qType, 2 >, std::vector< std::vector< std::map< qType, OperatorType > > > > > &O_in, const std::vector< Qbasis< Symmetry > > &qAux_in, const std::vector< std::vector< qType > > &qPhys_in, const bool FINALIZED_IN, const BC boundary_condition_in, const qType &qTot_in=Symmetry::qvacuum())

	MpoTerms (const std::size_t L=0, const BC boundary_condition_in=BC::OPEN, const qType &qTot_in=Symmetry::qvacuum(), const DMRG::VERBOSITY::OPTION &VERB_in=DMRG::VERBOSITY::OPTION::SILENT)

void	initialize (const std::size_t L, const BC boundary_condition_in, const qType &qTot_in)

virtual void	push (const std::size_t loc, const std::vector< OperatorType > &opList, const std::vector< qType > &qList, const Scalar lambda=1.0)

void	push (const std::size_t loc, const std::vector< OperatorType > &opList, const Scalar lambda=1.0)

void	show () const

void	save_label (const std::size_t loc, const std::string &info_label)

void	set_name (const std::string &label_in)

const std::string	get_name () const

std::vector< std::string >	get_info () const

void	scale (const Scalar factor, const Scalar offset=0., const std::size_t power=0ul, const double tolerance=1.e-14)

template<typename OtherScalar >
MpoTerms< Symmetry, OtherScalar >	cast ()

void	set_qPhys (const std::size_t loc, const std::vector< qType > &qPhys_in)

void	finalize (const bool COMPRESS=true, const std::size_t power=1, const double tolerance=::mynumeric_limits< double >::epsilon())

void	calc (const std::size_t power)

bool	is_finalized () const

const std::vector< std::map< std::array< qType, 2 >, std::vector< std::vector< std::map< qType, OperatorType > > > > > &	get_O () const

const std::vector< std::vector< std::vector< std::vector< Biped< Symmetry, MatrixType > > > > > &	get_W () const

const std::vector< Qbasis< Symmetry > > &	get_qAux () const

const std::vector< std::vector< qType > > &	get_qOp () const

const std::vector< std::vector< qType > > &	get_qPhys () const

const std::vector< std::vector< std::vector< std::vector< Biped< Symmetry, MatrixType > > > > > &	get_W_power (std::size_t power) const

const std::vector< Qbasis< Symmetry > > &	get_qAux_power (std::size_t power) const

const std::vector< std::vector< qType > > &	get_qOp_power (std::size_t power) const

std::size_t	get_hilbert_dimension (const std::size_t loc) const

BC	get_boundary_condition () const

const qType &	get_qVac () const

const qType &	get_qTot () const

const std::size_t	get_pos_qTot () const

bool	check_qPhys () const

bool	check_power (std::size_t power) const

std::size_t	maxPower () const

std::size_t	size () const

void	transform_base (const qType &qShift, const bool PRINT=false, const int factor=-1, const std::size_t powre=0ul)

std::vector< std::vector< TwoSiteData< Symmetry, Scalar > > >	calc_TwoSiteData () const

std::vector< std::pair< qType, std::size_t > >	base_order_IBC (const std::size_t power=1) const

double	memory (MEMUNIT memunit=kB) const

double	sparsity (const std::size_t power=1, const bool PER_MATRIX=false) const

void	set_Identity (const typename Symmetry::qType &Q=Symmetry::qvacuum())

void	set_Zero ()

void	set_verbosity (const DMRG::VERBOSITY::OPTION VERB_in)

DMRG::VERBOSITY::OPTION	get_verbosity () const

void	save (std::string filename)

void	load (std::string filename)

const std::vector< std::vector< std::vector< Biped< Symmetry, MatrixType > > > > &	W_at (const std::size_t loc) const

const std::vector< std::vector< std::vector< std::vector< Biped< Symmetry, MatrixType > > > > > &	W_full () const

const std::vector< std::vector< qType > > &	locBasis () const

const std::vector< qType > &	locBasis (const std::size_t loc) const

const std::vector< Qbasis< Symmetry > > &	auxBasis () const

const Qbasis< Symmetry > &	auxBasis (const std::size_t loc) const

const Qbasis< Symmetry > &	inBasis (const std::size_t loc) const

const Qbasis< Symmetry > &	outBasis (const std::size_t loc) const

const std::vector< std::vector< qType > > &	opBasis () const

const std::vector< qType > &	opBasis (const std::size_t loc) const

const qType &	Qtarget () const

void	setLocBasis (const std::vector< std::vector< qType > > &q)

void	setLocBasis (const std::vector< qType > &q, std::size_t loc)

const std::vector< std::vector< std::vector< Biped< Symmetry, MatrixType > > > > &	Wsq_at (const std::size_t loc) const

const std::vector< qType > &	opBasisSq (const std::size_t loc) const

const std::vector< std::vector< qType > > &	opBasisSq () const

const bool	check_SQUARE () const

double	sparsity (bool USE_SQUARE, bool PER_MATRIX) const

void	setQtarget (const qType &q)

Public Member Functions inherited from SpinlessFermionsObservables< Sym::ZN< Sym::ChargeZ2, 2 > >
	SpinlessFermionsObservables ()

	SpinlessFermionsObservables (const size_t &L)

	SpinlessFermionsObservables (const size_t &L, const vector< Param > &params, const std::map< string, std::any > &defaults)

Mpo< Sym::ZN< Sym::ChargeZ2, 2 >, double >	c (size_t locx, size_t locy=0) const

Mpo< Sym::ZN< Sym::ChargeZ2, 2 >, double >	cdag (size_t locx, size_t locy=0) const

Mpo< Sym::ZN< Sym::ChargeZ2, 2 >, double >	n (size_t locx, size_t locy=0) const

Mpo< Sym::ZN< Sym::ChargeZ2, 2 >, double >	nph (size_t locx, size_t locy=0) const

Mpo< Sym::ZN< Sym::ChargeZ2, 2 >, double >	nn (size_t locx1, size_t locx2, size_t locy1=0, size_t locy2=0) const

Public Member Functions inherited from ParamReturner
	ParamReturner ()

	ParamReturner (const std::map< string, std::any > &defaults_input)

DMRG::CONTROL::DYN	get_DmrgDynParam (const vector< Param > &params={}) const

DMRG::CONTROL::GLOB	get_DmrgGlobParam (const vector< Param > &params={}) const

VUMPS::CONTROL::DYN	get_VumpsDynParam (const vector< Param > &params={}) const

VUMPS::CONTROL::GLOB	get_VumpsGlobParam (const vector< Param > &params={}) const

Static Public Member Functions
static qarray< 1 >	singlet (int N)

template<typename Symmetry_ >
static void	add_operators (const std::vector< SpinlessFermionBase< Symmetry_ > > &B, const ParamHandler &P, HamiltonianTermsXd< Symmetry_ > &Terms)

Static Public Member Functions inherited from Mpo< Sym::ZN< Sym::ChargeZ2, 2 > >
static std::vector< T >	get_N_site_interaction (T const &Op0, Operator const &... Ops)

static Mpo< Sym::ZN< Sym::ChargeZ2, 2 >, double >	Identity (const std::vector< std::vector< qType > > &qPhys, const qType &Q=Symmetry::qvacuum())

static Mpo< Sym::ZN< Sym::ChargeZ2, 2 >, double >	Zero (const std::vector< std::vector< qType > > &qPhys)

static Mpo< Sym::ZN< Sym::ChargeZ2, 2 >, double >	cast_Terms_to_Mpo (const MpoTerms< Sym::ZN< Sym::ChargeZ2, 2 >, double > &input)

Static Public Member Functions inherited from MpoTerms< Symmetry, Scalar >
static MpoTerms< Symmetry, Scalar >	prod (const MpoTerms< Symmetry, Scalar > &top, const MpoTerms< Symmetry, Scalar > &bottom, const qType &qTot, const double tolerance=::mynumeric_limits< double >::epsilon())

static MpoTerms< Symmetry, Scalar >	sum (const MpoTerms< Symmetry, Scalar > &top, const MpoTerms< Symmetry, Scalar > &bottom, const double tolerance=::mynumeric_limits< double >::epsilon())

Static Public Attributes
static constexpr MODEL_FAMILY	FAMILY = SPINLESS

static const std::map< string, std::any >	defaults

static const std::map< string, std::any >	sweep_defaults

Static Public Attributes inherited from Mpo< Sym::ZN< Sym::ChargeZ2, 2 > >
static constexpr size_t	Nq

Private Types
typedef Symmetry::qType	qType

Additional Inherited Members
Public Attributes inherited from Mpo< Sym::ZN< Sym::ChargeZ2, 2 > >
Symmetry::qType	qVac

bool	GOT_TWO_SITE_DATA

std::vector< std::vector< TwoSiteData< Sym::ZN< Sym::ChargeZ2, 2 >, double > > >	TSD

bool	UNITARY

bool	HERMITIAN

bool	HAMILTONIAN

bool	GOT_SEMIOPEN_LEFT

bool	GOT_SEMIOPEN_RIGHT

OperatorType	LocalOp

int	LocalSite

Public Attributes inherited from MpoTerms< Symmetry, Scalar >
std::vector< std::vector< qType > >	qOp

std::vector< Qbasis< Symmetry > >	qAux

std::vector< std::vector< qType > >	qPhys

std::vector< std::vector< std::vector< std::vector< Biped< Symmetry, MatrixType > > > > >	W

std::vector< std::vector< std::vector< qType > > >	qOp_powers

std::vector< std::vector< Qbasis< Symmetry > > >	qAux_powers

std::vector< std::vector< std::vector< std::vector< std::vector< Biped< Symmetry, MatrixType > > > > > >	W_powers

std::size_t	N_sites

std::size_t	N_phys = 0ul

reversedData	reversed

std::string	label = "MPO"

Protected Member Functions inherited from MpoTerms< Symmetry, Scalar >
void	increment_auxdim (const std::size_t loc, const qType &q)

void	increment_first_auxdim_OBC (const qType &qIn)

void	increment_last_auxdim_OBC (const qType &qOut)

void	decrement_auxdim (const std::size_t loc, const qType &q)

void	decrement_first_auxdim_OBC (const qType &qIn)

void	decrement_last_auxdim_OBC (const qType &qOut)

void	add (const std::size_t loc, const OperatorType &op, const qType &qIn, const qType &qOut, const std::size_t IndexIn, const std::size_t IndexOut)

std::size_t	get_auxdim (const std::size_t loc, const qType &q) const

void	assert_hilbert (const std::size_t loc, const std::size_t dim)

bool	eliminate_linearlyDependent_rows (const std::size_t loc, const qType &qIn, const double tolerance)

bool	eliminate_linearlyDependent_cols (const std::size_t loc, const qType &qOut, const double tolerance)

std::map< qType, std::vector< std::map< qType, OperatorType > > >	delete_row (const std::size_t loc, const qType &qIn, const std::size_t row_to_delete, const bool SAMESITE)

std::map< qType, std::vector< std::map< qType, OperatorType > > >	delete_col (const std::size_t loc, const qType &qOut, const std::size_t col_to_delete, const bool SAMESITE)

void	add_to_row (const std::size_t loc, const qType &qIn, const std::size_t row, const std::map< qType, std::vector< std::map< qType, OperatorType > > > &ops, const Scalar factor)

void	add_to_col (const std::size_t loc, const qType &qOut, const std::size_t col, const std::map< qType, std::vector< std::map< qType, OperatorType > > > &ops, const Scalar factor)

void	calc_qOp ()

void	calc_qAux ()

void	calc_W ()

void	got_update ()

void	initialize ()

void	compress (const double tolerance)

void	renormalize ()

void	clear_opLabels ()

std::tuple< std::size_t, std::size_t, std::size_t, std::size_t >	auxdim_infos () const

std::vector< qType >	calc_qList (const std::vector< OperatorType > &opList)

void	fill_O_from_W ()

Protected Member Functions inherited from SpinlessFermionsObservables< Sym::ZN< Sym::ChargeZ2, 2 > >
Mpo< Sym::ZN< Sym::ChargeZ2, 2 >, double >	make_local (size_t locx, size_t locy, const OperatorType &Op, double factor, bool FERMIONIC=false, bool HERMITIAN=false) const

Mpo< Sym::ZN< Sym::ChargeZ2, 2 >, double >	make_corr (string name1, string name2, size_t locx1, size_t locx2, size_t locy1, size_t locy2, const OperatorType &Op1, const OperatorType &Op2, bool BOTH_HERMITIAN=false) const

Static Protected Member Functions inherited from MpoTerms< Symmetry, Scalar >
static void	prod_swap_IBC (std::vector< std::map< std::array< qType, 2 >, std::vector< std::vector< std::map< qType, OperatorType > > > > > &O_out, std::vector< std::size_t > &row_qVac, std::vector< std::size_t > &col_qVac, std::vector< std::size_t > &row_qTot, std::vector< std::size_t > &col_qTot)

static void	prod_delZeroCols_OBC (std::map< std::array< qType, 2 >, std::vector< std::vector< std::map< qType, OperatorType > > > > &O_last, Qbasis< Symmetry > &qAux_last, Qbasis< Symmetry > &qAux_prev, const qType &qTot, const std::size_t col_qTot)

static std::string	power_to_string (std::size_t power)

static std::pair< std::string, std::size_t >	detect_and_remove_power (const std::string &name_w_power)

Protected Attributes inherited from MpoTerms< Symmetry, Scalar >
std::vector< std::map< std::array< qType, 2 >, std::vector< std::vector< std::map< qType, OperatorType > > > > >	O

std::vector< std::map< qType, std::size_t > >	auxdim

qType	qTot

qType	qVac = Symmetry::qvacuum()

std::size_t	pos_qTot

std::size_t	pos_qVac

BC	boundary_condition

std::vector< std::vector< std::string > >	info

std::vector< int >	hilbert_dimension

MPO_STATUS::OPTION	status = MPO_STATUS::ALTERABLE

DMRG::VERBOSITY::OPTION	VERB = DMRG::VERBOSITY::OPTION::SILENT

std::string	before_verb_set

std::size_t	current_power = 1

bool	GOT_QOP = false

bool	GOT_QAUX = false

bool	GOT_W = false

std::vector< bool >	GOT_QPHYS

Protected Attributes inherited from SpinlessFermionsObservables< Sym::ZN< Sym::ChargeZ2, 2 > >
vector< SpinlessFermionBase< Sym::ZN< Sym::ChargeZ2, 2 > > >	F

Member Typedef Documentation

◆ qType

typedef Symmetry::qType VMPS::SpinlessFermionsZ2::qType

private

Definition at line 33 of file SpinlessFermionsZ2.h.

◆ Symmetry

typedef Sym::ZN<Sym::ChargeZ2,2> VMPS::SpinlessFermionsZ2::Symmetry

Definition at line 29 of file SpinlessFermionsZ2.h.

Constructor & Destructor Documentation

◆ SpinlessFermionsZ2() [1/2]

VMPS::SpinlessFermionsZ2::SpinlessFermionsZ2 ( )

inline

Definition at line 38 of file SpinlessFermionsZ2.h.

◆ SpinlessFermionsZ2() [2/2]

VMPS::SpinlessFermionsZ2::SpinlessFermionsZ2	(	const size_t &	L,
		const vector< Param > &	params
	)

Definition at line 72 of file SpinlessFermionsZ2.h.

Member Function Documentation

◆ add_operators()

template<typename Symmetry_ >

void VMPS::SpinlessFermionsZ2::add_operators	(	const std::vector< SpinlessFermionBase< Symmetry_ > > &	B,
		const ParamHandler &	P,
		HamiltonianTermsXd< Symmetry_ > &	Terms
	)

static

Definition at line 96 of file SpinlessFermionsZ2.h.

◆ singlet()

static qarray< 1 > VMPS::SpinlessFermionsZ2::singlet ( int N )

inlinestatic

Definition at line 42 of file SpinlessFermionsZ2.h.

Member Data Documentation

◆ defaults

const std::map< string, std::any > VMPS::SpinlessFermionsZ2::defaults

static

Initial value:

= 
{
    {"t",1.}, {"Delta",0.}, {"tPrime",0.},
    {"V",0.}, {"Vph",0.},
    {"Vprime",0.}, {"VphPrime",0.},
    {"mu",0.},{"t0",0.},
    {"D",2ul}, {"CALC_SQUARE",true}, {"CYLINDER",false}, {"OPEN_BC",true}, {"Ly",1ul}, 
}

Definition at line 48 of file SpinlessFermionsZ2.h.

◆ FAMILY

constexpr MODEL_FAMILY VMPS::SpinlessFermionsZ2::FAMILY = SPINLESS

staticconstexpr

Definition at line 43 of file SpinlessFermionsZ2.h.

◆ sweep_defaults

const std::map< string, std::any > VMPS::SpinlessFermionsZ2::sweep_defaults

static

Initial value:

= 
{
    {"max_alpha",100.}, {"min_alpha",1.e-11}, {"lim_alpha",10ul}, {"eps_svd",1.e-7},
    {"Dincr_abs", 4ul}, {"Dincr_per", 2ul}, {"Dincr_rel", 1.1},
    {"min_Nsv",0ul}, {"max_Nrich",-1},
    {"max_halfsweeps",40ul}, {"min_halfsweeps",1ul},
    {"Dinit",10ul}, {"Qinit",2ul}, {"Dlimit",1000ul},
    {"tol_eigval",1.e-5}, {"tol_state",1.e-5},
    {"savePeriod",0ul}, {"CALC_S_ON_EXIT", true}, {"CONVTEST", DMRG::CONVTEST::VAR_2SITE}
}

Definition at line 49 of file SpinlessFermionsZ2.h.

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

SpinlessFermionsZ2.h

Detailed Description

Public Types

Public Member Functions

Static Public Member Functions

Static Public Attributes

Private Types

Additional Inherited Members

Member Typedef Documentation

◆ qType

◆ Symmetry

Constructor & Destructor Documentation

◆ SpinlessFermionsZ2() [1/2]

◆ SpinlessFermionsZ2() [2/2]

Member Function Documentation

◆ add_operators()

◆ singlet()

Member Data Documentation

◆ defaults

◆ FAMILY

◆ sweep_defaults