mps-0.0.0 MatrixProductStatesinC++
mps::iTEBD< Tensor > Class Template Reference

An infinite Matrix Product State with translational invariance but using two tensors: one for odd and one for even sites. More...

## Public Member Functions

const iTEBD< Tensor > apply_operator (const Tensor &U, int odd=0, double tolerance=-1, tensor::index max_dim=0) const
Construct a new state after acting on 'odd' or 'even' pair of sites with the two-site operator U. More...

const iTEBD< Tensor > canonical_form (double tolerance=-1, tensor::index max_dim=0) const
Return a new state which is in canonical form. More...

const Tensor & combined_matrix (int site) const
Fold a matrix with its neighboring vector . More...

double entropy (int site) const
Estimate the entanglement entropy associated to splitting the state around 'site'.

double entropy () const
Average entropy for even and odd sites. More...

bool is_canonical () const
Is this iTEBD state in canonical form?

iTEBD (tensor::index dimension)
Create an random iTEBD state with given physical dimensions. More...

iTEBD (const Tensor &newA)
Create a product state iTEBD. More...

iTEBD (const Tensor &newA, const Tensor &newB)
Create a product state iTEBD with two wavefunctions. More...

iTEBD (const Tensor &newA, const Tensor &newlA, const Tensor &newB, const Tensor &newlB, bool canonical=false)
Create an iTEBD with and matrices. More...

tensor::index left_dimension (int site) const
Return dimension of the MPS to the left of this site. More...

const Tensor & left_vector (int site) const
Return the vector to the left of this site. More...

const Tensor & matrix (int site) const
Return the matrix for the lattice 'site'. More...

tensor::index right_dimension (int site) const
Return dimension of the MPS to the right of this site. More...

const Tensor & right_vector (int site) const
Return the vector to the right of this site. More...

const Tensor schmidt (int site=0) const
Schmidt numbers. More...

tensor::index site_dimension (int site) const
Physical dimension of the given site. More...

## Detailed Description

### template<class Tensor> class mps::iTEBD< Tensor >

An infinite Matrix Product State with translational invariance but using two tensors: one for odd and one for even sites.

This algorithm follows the iTBD implementation sketched by R. Orus and G. Vidal in Phys. Rev. B 78, 155117 (2008)

Definition at line 41 of file itebd.h.

## Constructor & Destructor Documentation

template<class Tensor >
 mps::iTEBD< Tensor >::iTEBD ( tensor::index dimension )
explicit

Create an random iTEBD state with given physical dimensions.

Definition at line 34 of file itebd.hpp.

template<class Tensor >
 mps::iTEBD< Tensor >::iTEBD ( const Tensor & newA )

Create a product state iTEBD.

Definition at line 45 of file itebd.hpp.

template<class Tensor >
 mps::iTEBD< Tensor >::iTEBD ( const Tensor & newA, const Tensor & newB )

Create a product state iTEBD with two wavefunctions.

Definition at line 56 of file itebd.hpp.

template<class Tensor >
 mps::iTEBD< Tensor >::iTEBD ( const Tensor & newA, const Tensor & newlA, const Tensor & newB, const Tensor & newlB, bool canonical = false )

Create an iTEBD with and matrices.

Definition at line 68 of file itebd.hpp.

## Member Function Documentation

template<class Tensor >
 const iTEBD< Tensor > mps::iTEBD< Tensor >::apply_operator ( const Tensor & U, int odd = 0, double tolerance = -1, tensor::index max_dim = 0 ) const

Construct a new state after acting on 'odd' or 'even' pair of sites with the two-site operator U.

Definition at line 316 of file itebd_canonical.hpp.

template<class Tensor >
 const iTEBD< Tensor > mps::iTEBD< Tensor >::canonical_form ( double tolerance = -1, tensor::index max_dim = 0 ) const

Return a new state which is in canonical form.

Definition at line 261 of file itebd_canonical.hpp.

template<class Tensor>
 const Tensor& mps::iTEBD< Tensor >::combined_matrix ( int site ) const
inline

Fold a matrix with its neighboring vector .

Definition at line 93 of file itebd.h.

template<class Tensor>
 double mps::iTEBD< Tensor >::entropy ( ) const
inline

Average entropy for even and odd sites.

Definition at line 79 of file itebd.h.

template<class Tensor>
 tensor::index mps::iTEBD< Tensor >::left_dimension ( int site ) const
inline

Return dimension of the MPS to the left of this site.

Definition at line 113 of file itebd.h.

template<class Tensor>
 const Tensor& mps::iTEBD< Tensor >::left_vector ( int site ) const
inline

Return the vector to the left of this site.

Definition at line 98 of file itebd.h.

template<class Tensor>
 const Tensor& mps::iTEBD< Tensor >::matrix ( int site ) const
inline

Return the matrix for the lattice 'site'.

Definition at line 88 of file itebd.h.

template<class Tensor>
 tensor::index mps::iTEBD< Tensor >::right_dimension ( int site ) const
inline

Return dimension of the MPS to the right of this site.

Definition at line 118 of file itebd.h.

template<class Tensor>
 const Tensor& mps::iTEBD< Tensor >::right_vector ( int site ) const
inline

Return the vector to the right of this site.

Definition at line 103 of file itebd.h.

template<class Tensor >
 const Tensor mps::iTEBD< Tensor >::schmidt ( int site = 0 ) const

Schmidt numbers.

Definition at line 95 of file itebd.hpp.

template<class Tensor>
 tensor::index mps::iTEBD< Tensor >::site_dimension ( int site ) const
inline

Physical dimension of the given site.

Definition at line 108 of file itebd.h.