Detailed Description

template<typename Symmetry, typename Scalar = double>
class Umps< Symmetry, Scalar >

Uniform Matrix Product State. Analogue of the Mps class.

Template Parameters

Symmetry	: A class providing all relevant functions and infos that are determined by the Symmetry. Click here for more information.
Scalar	: `double` or `complex<double>`

Definition at line 41 of file Umps.h.

#include <Umps.h>

Public Member Functions
	Umps ()

template<typename Hamiltonian >
	Umps (const Hamiltonian &H, qarray< Nq > Qtot_input, size_t L_input, size_t Mmax, size_t Nqmax, bool INIT_TO_HALF_INTEGER_SPIN)

	Umps (const vector< qarray< Symmetry::Nq > > &qloc_input, qarray< Nq > Qtot_input, size_t L_input, size_t Mmax, size_t Nqmax, bool INIT_TO_HALF_INTEGER_SPIN)

	Umps (const vector< vector< qarray< Symmetry::Nq > > > &qloc_input, qarray< Nq > Qtot_input, size_t L_input, size_t Mmax, size_t Nqmax, bool INIT_TO_HALF_INTEGER_SPIN)

string	info () const

void	graph (string filename) const

string	test_ortho (double tol=1e-6) const

void	setRandom ()

void	normalize_C ()

void	resize (size_t Mmax_input, size_t Nqmax_input, bool INIT_TO_HALF_INTEGER_SPIN)

template<typename OtherMatrixType >
void	resize (const Umps< Symmetry, OtherMatrixType > &V)

void	resize_arrays ()

void	svdDecompose (size_t loc, GAUGE::OPTION gauge=GAUGE::C)

void	polarDecompose (size_t loc, GAUGE::OPTION gauge=GAUGE::C)

VectorXd	entropy () const

vector< map< qarray< Nq >, tuple< ArrayXd, int > > >	entanglementSpectrum () const

std::pair< vector< qarray< Symmetry::Nq > >, ArrayXd >	entanglementSpectrumLoc (size_t loc) const

template<typename OtherScalar >
Umps< Symmetry, OtherScalar >	cast () const

Umps< Symmetry, double >	real () const

vector< qarray< Symmetry::Nq > >	locBasis (size_t loc) const

vector< vector< qarray< Symmetry::Nq > > >	locBasis () const

Qbasis< Symmetry >	inBasis (size_t loc) const

vector< Qbasis< Symmetry > >	inBasis () const

Qbasis< Symmetry >	outBasis (size_t loc) const

vector< Qbasis< Symmetry > >	outBasis () const

size_t	get_frst_rows () const

size_t	get_last_cols () const

size_t	length () const

Scalar	calc_epsLRsq (GAUGE::OPTION gauge, size_t loc) const

size_t	calc_Mmax () const

size_t	calc_fullMmax () const

size_t	calc_Dmax () const

size_t	calc_Nqmax () const

double	memory (MEMUNIT memunit) const

double	dot (const Umps< Symmetry, Scalar > &Vket) const

const vector< Biped< Symmetry, MatrixType > > &	A_at (GAUGE::OPTION g, size_t loc) const

qarray< Symmetry::Nq >	Qtop (size_t loc) const

qarray< Symmetry::Nq >	Qbot (size_t loc) const

size_t	minus1modL (size_t l) const

qarray< Nq >	Qtarget () const

void	calc_N (DMRG::DIRECTION::OPTION DIR, size_t loc, vector< Biped< Symmetry, MatrixType > > &N) const

void	truncate (bool SET_AC_RANDOM=true)

void	orthogonalize_left (GAUGE::OPTION g, vector< Biped< Symmetry, MatrixType > > &G_L)

void	orthogonalize_right (GAUGE::OPTION g, vector< Biped< Symmetry, MatrixType > > &G_R)

std::pair< complex< double >, Biped< Symmetry, Matrix< complex< double >, Dynamic, Dynamic > > >	calc_dominant_1symm (GAUGE::OPTION g, DMRG::DIRECTION::OPTION DIR, const Mpo< Symmetry, complex< double > > &R, bool TRANSPOSE, bool CONJUGATE) const

std::pair< complex< double >, Biped< Symmetry, Matrix< complex< double >, Dynamic, Dynamic > > >	calc_dominant_2symm (GAUGE::OPTION g, DMRG::DIRECTION::OPTION DIR, const Mpo< Symmetry, complex< double > > &R1, const Mpo< Symmetry, complex< double > > &R2) const

vector< std::pair< complex< double >, Biped< Symmetry, Matrix< complex< double >, Dynamic, Dynamic > > > >	calc_dominant (GAUGE::OPTION g=GAUGE::R, DMRG::DIRECTION::OPTION DIR=DMRG::DIRECTION::RIGHT, int N=2, double tol=1e-15, int dimK=-1, qarray< Symmetry::Nq > Qtot=Symmetry::qvacuum(), string label="") const

template<typename MpoScalar >
vector< std::pair< complex< double >, Tripod< Symmetry, Matrix< complex< double >, Dynamic, Dynamic > > > >	calc_dominant_Q (const Mpo< Symmetry, MpoScalar > &O, GAUGE::OPTION g=GAUGE::R, DMRG::DIRECTION::OPTION DIR=DMRG::DIRECTION::RIGHT, int N=2, double tol=1e-15, int dimK=-1, string label="") const

void	adjustQN (const size_t number_cells)

void	sort_A (size_t loc, GAUGE::OPTION g, bool SORT_ALL_GAUGES=false)

void	updateC (size_t loc)

void	updateAC (size_t loc, GAUGE::OPTION g)

void	enrich (size_t loc, GAUGE::OPTION g, const vector< Biped< Symmetry, MatrixType > > &P)

template<typename MpoScalar >
ArrayXXcd	intercellSF (const Mpo< Symmetry, MpoScalar > &Oalfa, const Mpo< Symmetry, MpoScalar > &Obeta, int Lx, double kmin=0., double kmax=2.*M_PI, int kpoints=51, DMRG::VERBOSITY::OPTION VERB=DMRG::VERBOSITY::ON_EXIT, double tol=1e-12)

template<typename MpoScalar >
complex< Scalar >	intercellSFpoint (const Mpo< Symmetry, MpoScalar > &Oalfa, const Mpo< Symmetry, MpoScalar > &Obeta, int Lx, double kval, DMRG::VERBOSITY::OPTION VERB=DMRG::VERBOSITY::ON_EXIT)

template<typename MpoScalar >
ArrayXXcd	SF (const ArrayXXcd &cellAvg, const vector< Mpo< Symmetry, MpoScalar > > &Oalfa, const vector< Mpo< Symmetry, MpoScalar > > &Obeta, int Lx, double kmin, double kmax, int kpoints, DMRG::VERBOSITY::OPTION VERB=DMRG::VERBOSITY::ON_EXIT, double tol=1e-12)

template<typename MpoScalar >
complex< Scalar >	SFpoint (const ArrayXXcd &cellAvg, const vector< Mpo< Symmetry, MpoScalar > > &Oalfa, const vector< Mpo< Symmetry, MpoScalar > > &Obeta, int Lx, double kval, DMRG::VERBOSITY::OPTION VERB=DMRG::VERBOSITY::ON_EXIT)

void	calc_entropy (size_t loc, bool PRINT=false)

void	calc_entropy (bool PRINT=false)

void	update_inbase (size_t loc, GAUGE::OPTION g=GAUGE::C)

void	update_outbase (size_t loc, GAUGE::OPTION g=GAUGE::C)

void	update_inbase (GAUGE::OPTION g=GAUGE::C)

void	update_outbase (GAUGE::OPTION g=GAUGE::C)

Public Attributes
size_t	N_sites

size_t	Mmax

size_t	Nqmax

double	eps_svd = 1e-13

double	eps_truncWeight = 1e-14

size_t	max_Nsv =100000ul

size_t	min_Nsv =1ul

int	max_Nrich

qarray< Nq >	Qtot

ArrayXd	truncWeight

vector< vector< qarray< Symmetry::Nq > > >	qloc

std::array< vector< vector< Biped< Symmetry, MatrixType > > >, 3 >	A

vector< Biped< Symmetry, MatrixType > >	C

VectorXd	S

vector< map< qarray< Nq >, tuple< ArrayXd, int > > >	SVspec

vector< Qbasis< Symmetry > >	inbase

vector< Qbasis< Symmetry > >	outbase

Private Types
typedef Matrix< Scalar, Dynamic, Dynamic >	MatrixType

Static Private Attributes
static constexpr size_t	Nq = Symmetry::Nq

Friends
template<typename Symmetry_ , typename MpHamiltonian , typename Scalar_ >
class	VumpsSolver

template<typename Symmetry_ , typename S1 , typename S2 >
class	MpsCompressor

Member Typedef Documentation

◆ MatrixType

template<typename Symmetry , typename Scalar = double>

typedef Matrix<Scalar,Dynamic,Dynamic> Umps< Symmetry, Scalar >::MatrixType

private

Definition at line 43 of file Umps.h.

Constructor & Destructor Documentation

◆ Umps() [1/4]

template<typename Symmetry , typename Scalar = double>

Umps< Symmetry, Scalar >::Umps ( )

inline

Does nothing.

Definition at line 52 of file Umps.h.

◆ Umps() [2/4]

template<typename Symmetry , typename Scalar >

template<typename Hamiltonian >

Umps< Symmetry, Scalar >::Umps	(	const Hamiltonian &	H,
		qarray< Nq >	Qtot_input,
		size_t	L_input,
		size_t	Mmax,
		size_t	Nqmax,
		bool	INIT_TO_HALF_INTEGER_SPIN
	)

Constructs a Umps with fixed bond dimension with the info from the Hamiltonian.

Definition at line 425 of file Umps.h.

◆ Umps() [3/4]

template<typename Symmetry , typename Scalar >

Umps< Symmetry, Scalar >::Umps	(	const vector< qarray< Symmetry::Nq > > &	qloc_input,
		qarray< Nq >	Qtot_input,
		size_t	L_input,
		size_t	Mmax,
		size_t	Nqmax,
		bool	INIT_TO_HALF_INTEGER_SPIN
	)

Constructs a Umps with fixed bond dimension with a uniform given basis.

Definition at line 434 of file Umps.h.

◆ Umps() [4/4]

template<typename Symmetry , typename Scalar >

Umps< Symmetry, Scalar >::Umps	(	const vector< vector< qarray< Symmetry::Nq > > > &	qloc_input,
		qarray< Nq >	Qtot_input,
		size_t	L_input,
		size_t	Mmax,
		size_t	Nqmax,
		bool	INIT_TO_HALF_INTEGER_SPIN
	)

Constructs a Umps with fixed bond dimension with a given basis.

Definition at line 445 of file Umps.h.

Member Function Documentation

◆ A_at()

template<typename Symmetry , typename Scalar = double>

const vector< Biped< Symmetry, MatrixType > > & Umps< Symmetry, Scalar >::A_at	(	GAUGE::OPTION	g,
		size_t	loc
	)		const

inline

Returns $A_L$ , $A_R$ or $A_C$ at site loc as const ref.

Definition at line 201 of file Umps.h.

◆ adjustQN()

template<typename Symmetry , typename Scalar >

void Umps< Symmetry, Scalar >::adjustQN ( const size_t number_cells )

This functions transforms all quantum numbers in the Umps (Umps::qloc and QN in Umps::A) by $q \rightarrow q * N_{cells}$ . It is used for avg(Umps V, Mpo O, Umps V) in VumpsLinearAlgebra.h when O.length() > V.length(). In this case the quantum numbers in the Umps are transformed in correspondence with V.length() and this is incompatible with the quantum numbers in O.length() which are transformed in correspondence to O.length().

Parameters

number_cells : $N_{cells}$

Definition at line 2024 of file Umps.h.

◆ calc_Dmax()

template<typename Symmetry , typename Scalar >

size_t Umps< Symmetry, Scalar >::calc_Dmax

Determines the maximal amount of rows or columns per site and per subspace.

Definition at line 486 of file Umps.h.

◆ calc_dominant()

template<typename Symmetry , typename Scalar >

vector< std::pair< complex< double >, Biped< Symmetry, Matrix< complex< double >, Dynamic, Dynamic > > > > Umps< Symmetry, Scalar >::calc_dominant	(	GAUGE::OPTION	g = `GAUGE::R`,
		DMRG::DIRECTION::OPTION	DIR = `DMRG::DIRECTION::RIGHT`,
		int	N = `2`,
		double	tol = `1e-15`,
		int	dimK = `-1`,
		qarray< Symmetry::Nq >	Qtot = `Symmetry::qvacuum()`,
		string	label = `""`
	)		const

Definition at line 2763 of file Umps.h.

◆ calc_dominant_1symm()

template<typename Symmetry , typename Scalar >

std::pair< complex< double >, Biped< Symmetry, Matrix< complex< double >, Dynamic, Dynamic > > > Umps< Symmetry, Scalar >::calc_dominant_1symm	(	GAUGE::OPTION	g,
		DMRG::DIRECTION::OPTION	DIR,
		const Mpo< Symmetry, complex< double > > &	R,
		bool	TRANSPOSE,
		bool	CONJUGATE
	)		const

Calculates either the right or the left fixed point of the transfer-matrix build up with A-tensors in GAUGE g.

Parameters

g	: GAUGE to orthogonalize.
DIR	: LEFT or RIGHT fixed point.

Note: The return values are of type complex<double>. Can we choose them sometimes to be real?

Definition at line 2933 of file Umps.h.

◆ calc_dominant_2symm()

template<typename Symmetry , typename Scalar >

std::pair< complex< double >, Biped< Symmetry, Matrix< complex< double >, Dynamic, Dynamic > > > Umps< Symmetry, Scalar >::calc_dominant_2symm	(	GAUGE::OPTION	g,
		DMRG::DIRECTION::OPTION	DIR,
		const Mpo< Symmetry, complex< double > > &	R1,
		const Mpo< Symmetry, complex< double > > &	R2
	)		const

Definition at line 2985 of file Umps.h.

◆ calc_dominant_Q()

template<typename Symmetry , typename Scalar >

template<typename MpoScalar >

vector< std::pair< complex< double >, Tripod< Symmetry, Matrix< complex< double >, Dynamic, Dynamic > > > > Umps< Symmetry, Scalar >::calc_dominant_Q	(	const Mpo< Symmetry, MpoScalar > &	O,
		GAUGE::OPTION	g = `GAUGE::R`,
		DMRG::DIRECTION::OPTION	DIR = `DMRG::DIRECTION::RIGHT`,
		int	N = `2`,
		double	tol = `1e-15`,
		int	dimK = `-1`,
		string	label = `""`
	)		const

Definition at line 2844 of file Umps.h.

◆ calc_entropy() [1/2]

template<typename Symmetry , typename Scalar = double>

void Umps< Symmetry, Scalar >::calc_entropy ( bool PRINT = false )

inline

Calculate entropy for all sites.

Definition at line 359 of file Umps.h.

◆ calc_entropy() [2/2]

template<typename Symmetry , typename Scalar >

void Umps< Symmetry, Scalar >::calc_entropy	(	size_t	loc,
		bool	PRINT = `false`
	)

Calculate entropy at site loc.

Definition at line 1156 of file Umps.h.

◆ calc_epsLRsq()

template<typename Symmetry , typename Scalar >

Scalar Umps< Symmetry, Scalar >::calc_epsLRsq	(	GAUGE::OPTION	gauge,
		size_t	loc
	)		const

Calculates the left and right decomposition error as $\epsilon_L=\big|A_C-A_LC\big|^2$ and $\epsilon_R=\big|A_C-CA_R\big|^2$ (eq. (18)).

Definition at line 1223 of file Umps.h.

◆ calc_fullMmax()

template<typename Symmetry , typename Scalar >

std::size_t Umps< Symmetry, Scalar >::calc_fullMmax

For SU(2) symmetries, determines the equivalent U(1) bond dimension.

Definition at line 512 of file Umps.h.

◆ calc_Mmax()

template<typename Symmetry , typename Scalar >

size_t Umps< Symmetry, Scalar >::calc_Mmax

Determines the maximal bond dimension per site (sum of A.rows or A.cols over all subspaces).

Definition at line 499 of file Umps.h.

◆ calc_N()

template<typename Symmetry , typename Scalar >

void Umps< Symmetry, Scalar >::calc_N	(	DMRG::DIRECTION::OPTION	DIR,
		size_t	loc,
		vector< Biped< Symmetry, MatrixType > > &	N
	)		const

Definition at line 1781 of file Umps.h.

◆ calc_Nqmax()

template<typename Symmetry , typename Scalar >

size_t Umps< Symmetry, Scalar >::calc_Nqmax

Determines the maximal amount of subspaces per site.

Definition at line 473 of file Umps.h.

◆ cast()

template<typename Symmetry , typename Scalar >

template<typename OtherScalar >

Umps< Symmetry, OtherScalar > Umps< Symmetry, Scalar >::cast

Casts the matrices from Scalar to OtherScalar.

Definition at line 1972 of file Umps.h.

◆ dot()

template<typename Symmetry , typename Scalar >

double Umps< Symmetry, Scalar >::dot ( const Umps< Symmetry, Scalar > & Vket ) const

Calculates the scalar product with another Umps by finding the dominant eigenvalue of the transfer matrix. See arXiv:0804.2509 and Phys. Rev. B 78, 155117.

Definition at line 1121 of file Umps.h.

◆ enrich()

template<typename Symmetry , typename Scalar >

void Umps< Symmetry, Scalar >::enrich	(	size_t	loc,
		GAUGE::OPTION	g,
		const vector< Biped< Symmetry, MatrixType > > &	P
	)

Enlarges the tensors of the Umps with an enrichment tensor P and resizes everything necessary with zeros. The tensor P needs to be calculated in advance. This is done directly in the VumpsSolver.

Parameters

loc	: location of the site to enrich.
g	: The gauge to enrich. L means, we need to update site tensor at loc+1 accordingly. R means updating site loc-1 with zeros.
P	: the tensor with the enrichment. It is calculated after Eq. (A31).

Definition at line 2374 of file Umps.h.

◆ entanglementSpectrum()

template<typename Symmetry , typename Scalar = double>

vector< map< qarray< Nq >, tuple< ArrayXd, int > > > Umps< Symmetry, Scalar >::entanglementSpectrum ( ) const

inline

Return the full entanglement spectrum, resolved by subspace quantum number.

Definition at line 112 of file Umps.h.

◆ entanglementSpectrumLoc()

template<typename Symmetry , typename Scalar >

std::pair< vector< qarray< Symmetry::Nq > >, ArrayXd > Umps< Symmetry, Scalar >::entanglementSpectrumLoc ( size_t loc ) const

Return the entanglement spectrum at the site loc (values all subspaces merged and sorted).

Definition at line 3060 of file Umps.h.

◆ entropy()

template<typename Symmetry , typename Scalar = double>

VectorXd Umps< Symmetry, Scalar >::entropy ( ) const

inline

Returns the entropy for all sites.

Definition at line 109 of file Umps.h.

◆ get_frst_rows()

template<typename Symmetry , typename Scalar = double>

size_t Umps< Symmetry, Scalar >::get_frst_rows ( ) const

inline

Returns the amount of rows of first tensor. Useful for environment tensors in contractions.

Definition at line 141 of file Umps.h.

◆ get_last_cols()

template<typename Symmetry , typename Scalar = double>

size_t Umps< Symmetry, Scalar >::get_last_cols ( ) const

inline

Returns the amount of columns of last tensor. Useful for environment tensors in contractions.

Definition at line 144 of file Umps.h.

◆ graph()

template<typename Symmetry , typename Scalar >

void Umps< Symmetry, Scalar >::graph ( string filename ) const

Prints a graph. See Mps::graph.

Definition at line 899 of file Umps.h.

◆ inBasis() [1/2]

template<typename Symmetry , typename Scalar = double>

vector< Qbasis< Symmetry > > Umps< Symmetry, Scalar >::inBasis ( ) const

inline

Definition at line 134 of file Umps.h.

◆ inBasis() [2/2]

template<typename Symmetry , typename Scalar = double>

Qbasis< Symmetry > Umps< Symmetry, Scalar >::inBasis ( size_t loc ) const

inline

Returns the ingoing basis.

Definition at line 133 of file Umps.h.

◆ info()

template<typename Symmetry , typename Scalar >

string Umps< Symmetry, Scalar >::info

Prints some info about this class.

Definition at line 392 of file Umps.h.

◆ intercellSF()

template<typename Symmetry , typename Scalar >

template<typename MpoScalar >

ArrayXXcd Umps< Symmetry, Scalar >::intercellSF	(	const Mpo< Symmetry, MpoScalar > &	Oalfa,
		const Mpo< Symmetry, MpoScalar > &	Obeta,
		int	Lx,
		double	kmin = `0.`,
		double	kmax = `2.*M_PI`,
		int	kpoints = `51`,
		DMRG::VERBOSITY::OPTION	VERB = `DMRG::VERBOSITY::ON_EXIT`,
		double	tol = `1e-12`
	)

Calculates the static structure factor between cells according to "Tangent-space methods for uniform matrix product states" (2018), chapter 2.5.

Note: For unit cells, the Fourier transform is done between cells only, the sublattice indices are fixed by the Mpos Oalfa, Obeta.; The result has the k-values as the first column and the SSF as the second column.

Parameters

Oalfa	: first operator of correlation
Obeta	: second operator of correlation
Lx	: length of the unit cell in x-direction
kmin	: start with this k-value
kmax	: end with this k-value (include it)
kpoints	: number of equidistant points in interval
VERB	: how much information to print

Definition at line 3083 of file Umps.h.

◆ intercellSFpoint()

template<typename Symmetry , typename Scalar >

template<typename MpoScalar >

complex< Scalar > Umps< Symmetry, Scalar >::intercellSFpoint	(	const Mpo< Symmetry, MpoScalar > &	Oalfa,
		const Mpo< Symmetry, MpoScalar > &	Obeta,
		int	Lx,
		double	kval,
		DMRG::VERBOSITY::OPTION	VERB = `DMRG::VERBOSITY::ON_EXIT`
	)

Calculates the static structure factor between cells for one k-point only. See the more general function above.

Definition at line 3241 of file Umps.h.

◆ length()

template<typename Symmetry , typename Scalar = double>

size_t Umps< Symmetry, Scalar >::length ( ) const

inline

Returns the amount of sites, i.e. the size of the unit cell.

Definition at line 147 of file Umps.h.

◆ locBasis() [1/2]

template<typename Symmetry , typename Scalar = double>

vector< vector< qarray< Symmetry::Nq > > > Umps< Symmetry, Scalar >::locBasis ( ) const

inline

Definition at line 130 of file Umps.h.

◆ locBasis() [2/2]

template<typename Symmetry , typename Scalar = double>

vector< qarray< Symmetry::Nq > > Umps< Symmetry, Scalar >::locBasis ( size_t loc ) const

inline

Returns the local basis.

Definition at line 129 of file Umps.h.

◆ memory()

template<typename Symmetry , typename Scalar >

double Umps< Symmetry, Scalar >::memory ( MEMUNIT memunit ) const

Calculates the (theoretically) allocated memory (note: by default in GB).

Definition at line 456 of file Umps.h.

◆ minus1modL()

template<typename Symmetry , typename Scalar = double>

size_t Umps< Symmetry, Scalar >::minus1modL ( size_t l ) const

inline

Safely calculates $l-1 mod L$ without overflow for size_t.

Definition at line 208 of file Umps.h.

◆ normalize_C()

template<typename Symmetry , typename Scalar >

void Umps< Symmetry, Scalar >::normalize_C

Normalizes the state, so that $Tr C^{\dagger} C = 1$

Definition at line 851 of file Umps.h.

◆ orthogonalize_left()

template<typename Symmetry , typename Scalar >

void Umps< Symmetry, Scalar >::orthogonalize_left	(	GAUGE::OPTION	g,
		vector< Biped< Symmetry, MatrixType > > &	G_L
	)

Orthogonalize the tensor with GAUGE g to be left-orthonormal using algorithm 2 from https://arxiv.org/abs/1810.07006.

Parameters

g	: GAUGE to orthogonalize.
G_L	: Gauge-Transformation which performs the orthogonalization: $A[g] \rightarrow G_LA[g]G_L^{-1}$

Note: : Call this function with GAUGE::L to reorthogonalize AL.

Definition at line 2639 of file Umps.h.

◆ orthogonalize_right()

template<typename Symmetry , typename Scalar >

void Umps< Symmetry, Scalar >::orthogonalize_right	(	GAUGE::OPTION	g,
		vector< Biped< Symmetry, MatrixType > > &	G_R
	)

Orthogonalize the tensor with GAUGE g to be right-orthonormal using the analogue to algorithm 2 from https://arxiv.org/abs/1810.07006.

Parameters

g	: GAUGE to orthogonalize.
G_R	: Gauge-Transformation which performs the orthogonalization: $A[g] \rightarrow G_R^{-1}A[g]G_R$

Note: : Call this function with GAUGE::R to reorthogonalize AR.

Definition at line 2574 of file Umps.h.

◆ outBasis() [1/2]

template<typename Symmetry , typename Scalar = double>

vector< Qbasis< Symmetry > > Umps< Symmetry, Scalar >::outBasis ( ) const

inline

Definition at line 138 of file Umps.h.

◆ outBasis() [2/2]

template<typename Symmetry , typename Scalar = double>

Qbasis< Symmetry > Umps< Symmetry, Scalar >::outBasis ( size_t loc ) const

inline

Returns the outgoing basis.

Definition at line 137 of file Umps.h.

◆ polarDecompose()

template<typename Symmetry , typename Scalar >

void Umps< Symmetry, Scalar >::polarDecompose	(	size_t	loc,
		GAUGE::OPTION	gauge = `GAUGE::C`
	)

Calculates $A_L$ and $A_R$ from $A_C$ and $C$ at site loc using the polar decomposition (eq. (21),(22)). This is supposed to be non-optimal, but accurate.

Definition at line 1357 of file Umps.h.

◆ Qbot()

template<typename Symmetry , typename Scalar >

qarray< Symmetry::Nq > Umps< Symmetry, Scalar >::Qbot ( size_t loc ) const

Definition at line 548 of file Umps.h.

◆ Qtarget()

template<typename Symmetry , typename Scalar = double>

qarray< Nq > Umps< Symmetry, Scalar >::Qtarget ( ) const

inline

Returns the total quantum number of the Umps.

Definition at line 211 of file Umps.h.

◆ Qtop()

template<typename Symmetry , typename Scalar >

qarray< Symmetry::Nq > Umps< Symmetry, Scalar >::Qtop ( size_t loc ) const

quantum number bounds for compatibility in contract_AA

Definition at line 541 of file Umps.h.

◆ real()

template<typename Symmetry , typename Scalar >

Umps< Symmetry, double > Umps< Symmetry, Scalar >::real

Returns a real Umps containing the real part of this.

Warning: Does not check, whether the imaginary part is zero.

Definition at line 1998 of file Umps.h.

◆ resize() [1/2]

template<typename Symmetry , typename Scalar >

template<typename OtherMatrixType >

void Umps< Symmetry, Scalar >::resize ( const Umps< Symmetry, OtherMatrixType > & V )

Determines all subspace quantum numbers and resizes the containers for the blocks. Memory for the matrices remains uninitiated. Pulls info from another Mps.

Parameters

V	: chain length, local basis and target quantum number will be equal to this umps

Definition at line 582 of file Umps.h.

◆ resize() [2/2]

template<typename Symmetry , typename Scalar >

void Umps< Symmetry, Scalar >::resize	(	size_t	Mmax_input,
		size_t	Nqmax_input,
		bool	INIT_TO_HALF_INTEGER_SPIN
	)

Resizes the bond dimension to Dmax and sets Nqmax blocks per site.

Definition at line 622 of file Umps.h.

◆ resize_arrays()

template<typename Symmetry , typename Scalar >

void Umps< Symmetry, Scalar >::resize_arrays

Shorthand to resize all the relevant arrays: A, inbase, outbase, truncWeight, S.

Definition at line 555 of file Umps.h.

◆ setRandom()

template<typename Symmetry , typename Scalar >

void Umps< Symmetry, Scalar >::setRandom

Sets all matrices $A_L$ , $A_R$ , $A_C$ , $C$ ) to random using boost's uniform distribution from -1 to 1.

Definition at line 862 of file Umps.h.

◆ SF()

template<typename Symmetry , typename Scalar >

template<typename MpoScalar >

ArrayXXcd Umps< Symmetry, Scalar >::SF	(	const ArrayXXcd &	cellAvg,
		const vector< Mpo< Symmetry, MpoScalar > > &	Oalfa,
		const vector< Mpo< Symmetry, MpoScalar > > &	Obeta,
		int	Lx,
		double	kmin,
		double	kmax,
		int	kpoints,
		DMRG::VERBOSITY::OPTION	VERB = `DMRG::VERBOSITY::ON_EXIT`,
		double	tol = `1e-12`
	)

Calculates the full static structure factor for a range of k-points.

Parameters

cellAvg	: all expectation values within unit cell
Oalfa	: first operator of correlation at each cell point
Obeta	: second operator of correlation at each cell point
Lx	: length of the unit cell in x-direction
kmin	: start with this k-value
kmax	: end with this k-value (include it)
kpoints	: number of equidistant points in interval
VERB	: how much information to print

Definition at line 3282 of file Umps.h.

◆ SFpoint()

template<typename Symmetry , typename Scalar >

template<typename MpoScalar >

complex< Scalar > Umps< Symmetry, Scalar >::SFpoint	(	const ArrayXXcd &	cellAvg,
		const vector< Mpo< Symmetry, MpoScalar > > &	Oalfa,
		const vector< Mpo< Symmetry, MpoScalar > > &	Obeta,
		int	Lx,
		double	kval,
		DMRG::VERBOSITY::OPTION	VERB = `DMRG::VERBOSITY::ON_EXIT`
	)

Calculates the full static structure factor between cells for one k-point only. See the more general function above.

Definition at line 3250 of file Umps.h.

◆ sort_A()

template<typename Symmetry , typename Scalar >

void Umps< Symmetry, Scalar >::sort_A	(	size_t	loc,
		GAUGE::OPTION	g,
		bool	SORT_ALL_GAUGES = `false`
	)

Sorts the A tensors of a specific gauge. If SORT_ALL_GAUGES is true, then obviously all A tensors get sorted.

Definition at line 2295 of file Umps.h.

◆ svdDecompose()

template<typename Symmetry , typename Scalar >

void Umps< Symmetry, Scalar >::svdDecompose	(	size_t	loc,
		GAUGE::OPTION	gauge = `GAUGE::C`
	)

Calculates $A_L$ and $A_R$ from $A_C$ and $C$ at site loc using SVD (eqs. (19),(20)). This is supposed to be optimal, but not accurate.

Definition at line 1512 of file Umps.h.

◆ test_ortho()

template<typename Symmetry , typename Scalar >

string Umps< Symmetry, Scalar >::test_ortho ( double tol = 1e-6 ) const

Tests the orthogonality of the Umps.

Definition at line 971 of file Umps.h.

◆ truncate()

template<typename Symmetry , typename Scalar >

void Umps< Symmetry, Scalar >::truncate ( bool SET_AC_RANDOM = true )

Performs a truncation of an Umps by the singular values of the center-matrix C. Updates AL and AR with the truncated isometries from the SVD and reorthogonalize them afterwards.

Parameters

SET_AC_RANDOM : bool to decide, whether to set AC to random or to C*AR. Truncation of a converged Umps can be done with SET_AC_RANDOM=false to evaluate e.g. observables after the truncation. Truncation during the variational optimization should be done with SET_AC_RANDOM=true because otherwise this would be a bias.

Definition at line 2702 of file Umps.h.

◆ update_inbase() [1/2]

template<typename Symmetry , typename Scalar = double>

void Umps< Symmetry, Scalar >::update_inbase ( GAUGE::OPTION g = GAUGE::C )

inline

Definition at line 387 of file Umps.h.

◆ update_inbase() [2/2]

template<typename Symmetry , typename Scalar >

void Umps< Symmetry, Scalar >::update_inbase	(	size_t	loc,
		GAUGE::OPTION	g = `GAUGE::C`
	)

update basis

Definition at line 525 of file Umps.h.

◆ update_outbase() [1/2]

template<typename Symmetry , typename Scalar = double>

void Umps< Symmetry, Scalar >::update_outbase ( GAUGE::OPTION g = GAUGE::C )

inline

Definition at line 388 of file Umps.h.

◆ update_outbase() [2/2]

template<typename Symmetry , typename Scalar >

void Umps< Symmetry, Scalar >::update_outbase	(	size_t	loc,
		GAUGE::OPTION	g = `GAUGE::C`
	)

Definition at line 533 of file Umps.h.

◆ updateAC()

template<typename Symmetry , typename Scalar >

void Umps< Symmetry, Scalar >::updateAC	(	size_t	loc,
		GAUGE::OPTION	g
	)

Updates the tensor AC with zeros if the auxiallary basis has changed, e.g. after an enrichment process

Parameters

loc	: location of the C tensor for the update.
g	: Pull information about changed dimension from either A[GAUGE::L] or A[GAUGE::R].

Warning: Do not insert g = GAUGE::C here.

Definition at line 2345 of file Umps.h.

◆ updateC()

template<typename Symmetry , typename Scalar >

void Umps< Symmetry, Scalar >::updateC ( size_t loc )

Updates the tensor C with zeros if the auxiallary basis has changed, e.g. after an enrichment process

Parameters

loc	: location of the C tensor for the update.

Definition at line 2316 of file Umps.h.

Friends And Related Function Documentation

◆ MpsCompressor

template<typename Symmetry , typename Scalar = double>

template<typename Symmetry_ , typename S1 , typename S2 >

friend class MpsCompressor

friend

Definition at line 47 of file Umps.h.

◆ VumpsSolver

template<typename Symmetry , typename Scalar = double>

template<typename Symmetry_ , typename MpHamiltonian , typename Scalar_ >

friend class VumpsSolver

friend

Definition at line 46 of file Umps.h.

Member Data Documentation

◆ A

template<typename Symmetry , typename Scalar = double>

std::array<vector<vector<Biped<Symmetry,MatrixType> > >,3> Umps< Symmetry, Scalar >::A

A-tensors in the three gauges L, R, C

Definition at line 368 of file Umps.h.

◆ C

template<typename Symmetry , typename Scalar = double>

vector<Biped<Symmetry,MatrixType> > Umps< Symmetry, Scalar >::C

center matrix C

Definition at line 371 of file Umps.h.

◆ eps_svd

template<typename Symmetry , typename Scalar = double>

double Umps< Symmetry, Scalar >::eps_svd = 1e-13

Definition at line 348 of file Umps.h.

◆ eps_truncWeight

template<typename Symmetry , typename Scalar = double>

double Umps< Symmetry, Scalar >::eps_truncWeight = 1e-14

Definition at line 349 of file Umps.h.

◆ inbase

template<typename Symmetry , typename Scalar = double>

vector<Qbasis<Symmetry> > Umps< Symmetry, Scalar >::inbase

bases on all ingoing and outgoing legs of the Umps

Definition at line 381 of file Umps.h.

◆ max_Nrich

template<typename Symmetry , typename Scalar = double>

int Umps< Symmetry, Scalar >::max_Nrich

Definition at line 351 of file Umps.h.

◆ max_Nsv

template<typename Symmetry , typename Scalar = double>

size_t Umps< Symmetry, Scalar >::max_Nsv =100000ul

Definition at line 350 of file Umps.h.

◆ min_Nsv

template<typename Symmetry , typename Scalar = double>

size_t Umps< Symmetry, Scalar >::min_Nsv =1ul

Definition at line 350 of file Umps.h.

◆ Mmax

template<typename Symmetry , typename Scalar = double>

size_t Umps< Symmetry, Scalar >::Mmax

Definition at line 347 of file Umps.h.

◆ N_sites

template<typename Symmetry , typename Scalar = double>

size_t Umps< Symmetry, Scalar >::N_sites

parameter

Definition at line 346 of file Umps.h.

◆ Nq

template<typename Symmetry , typename Scalar = double>

constexpr size_t Umps< Symmetry, Scalar >::Nq = Symmetry::Nq

staticconstexprprivate

Definition at line 44 of file Umps.h.

◆ Nqmax

template<typename Symmetry , typename Scalar = double>

size_t Umps< Symmetry, Scalar >::Nqmax

Definition at line 347 of file Umps.h.

◆ outbase

template<typename Symmetry , typename Scalar = double>

vector<Qbasis<Symmetry> > Umps< Symmetry, Scalar >::outbase

Definition at line 382 of file Umps.h.

◆ qloc

template<typename Symmetry , typename Scalar = double>

vector<vector<qarray<Symmetry::Nq> > > Umps< Symmetry, Scalar >::qloc

local basis

Definition at line 365 of file Umps.h.

◆ Qtot

template<typename Symmetry , typename Scalar = double>

qarray<Nq> Umps< Symmetry, Scalar >::Qtot

Definition at line 353 of file Umps.h.

◆ S

template<typename Symmetry , typename Scalar = double>

VectorXd Umps< Symmetry, Scalar >::S

null space (see eq. (25) and surrounding text)

Definition at line 376 of file Umps.h.

◆ SVspec

template<typename Symmetry , typename Scalar = double>

vector<map<qarray<Nq>,tuple<ArrayXd,int> > > Umps< Symmetry, Scalar >::SVspec

Definition at line 378 of file Umps.h.

◆ truncWeight

template<typename Symmetry , typename Scalar = double>

ArrayXd Umps< Symmetry, Scalar >::truncWeight

truncated weight

Definition at line 362 of file Umps.h.

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

Mpo.h
Umps.h

Detailed Description

Public Member Functions

Public Attributes

Private Types

Static Private Attributes

Friends

Member Typedef Documentation

◆ MatrixType

Constructor & Destructor Documentation

◆ Umps() [1/4]

◆ Umps() [2/4]

◆ Umps() [3/4]

◆ Umps() [4/4]

Member Function Documentation

◆ A_at()

◆ adjustQN()

◆ calc_Dmax()

◆ calc_dominant()

◆ calc_dominant_1symm()

◆ calc_dominant_2symm()

◆ calc_dominant_Q()

◆ calc_entropy() [1/2]

◆ calc_entropy() [2/2]

◆ calc_epsLRsq()

◆ calc_fullMmax()

◆ calc_Mmax()

◆ calc_N()

◆ calc_Nqmax()

◆ cast()

◆ dot()

◆ enrich()

◆ entanglementSpectrum()

◆ entanglementSpectrumLoc()

◆ entropy()

◆ get_frst_rows()

◆ get_last_cols()

◆ graph()

◆ inBasis() [1/2]

◆ inBasis() [2/2]

◆ info()

◆ intercellSF()

◆ intercellSFpoint()

◆ length()

◆ locBasis() [1/2]

◆ locBasis() [2/2]

◆ memory()

◆ minus1modL()

◆ normalize_C()

◆ orthogonalize_left()

◆ orthogonalize_right()

◆ outBasis() [1/2]

◆ outBasis() [2/2]

◆ polarDecompose()

◆ Qbot()

◆ Qtarget()

◆ Qtop()

◆ real()

◆ resize() [1/2]

◆ resize() [2/2]

◆ resize_arrays()

◆ setRandom()

◆ SF()

◆ SFpoint()

◆ sort_A()

◆ svdDecompose()

◆ test_ortho()

◆ truncate()

◆ update_inbase() [1/2]

◆ update_inbase() [2/2]

◆ update_outbase() [1/2]

◆ update_outbase() [2/2]

◆ updateAC()

◆ updateC()

Friends And Related Function Documentation

◆ MpsCompressor

◆ VumpsSolver

Member Data Documentation

◆ A

◆ C

◆ eps_svd