1.1. tnpy.exact_diagonalization.ExactDiagonalization#

class tnpy.exact_diagonalization.ExactDiagonalization(mpo, proj=None)[source]#

Bases: tnpy.operators.FullHamiltonian

Perform the numerically exact diagonalization on the matrix, which is constructed through the given Matrix Product Operator (MPO). Calculations are taken in prompt on the initialization of this class.

Parameters
Raises

ResourceWarning – When the dimensions of Hamiltonian are larger than \(4096 \times 4096\).

Examples

>>> ed = ExactDiagonalization(mpo)
>>> evals = ed.evals
>>> evecs = ed.evecs
__init__(mpo, proj=None)[source]#

Perform the numerically exact diagonalization on the matrix, which is constructed through the given Matrix Product Operator (MPO). Calculations are taken in prompt on the initialization of this class.

Parameters
Raises

ResourceWarning – When the dimensions of Hamiltonian are larger than \(4096 \times 4096\).

Examples

>>> ed = ExactDiagonalization(mpo)
>>> evals = ed.evals
>>> evecs = ed.evecs

Methods

__init__(mpo[, proj])

Perform the numerically exact diagonalization on the matrix, which is constructed through the given Matrix Product Operator (MPO).

connected_two_point_function(operator1, ...)

param operator1

entanglement_entropy(site[, level_idx, ...])

Compute the von Neumann entropy on the cutting site.

kron_operators(operators)

Perform Kronecker product on the given sequence of operators.

one_point_function(operator, site[, level_idx])

Compute the expectation value \(\langle \hat{O}_i \rangle\) of given local operator \(\hat{O}_i\) on site \(i\).

reduced_density_matrix(site[, level_idx])

Compute the reduced density matrix on the bi-partition site \(i\) through the singular value decomposition.

two_point_function(operator1, operator2, ...)

Compute the correlation function \(\langle \hat{O}_{i_1}^A \hat{O}_{i_2}^B \rangle\) of 2 given local operators \(\hat{O}_{i_1}^A\) and \(\hat{O}_{i_2}^B\) on site \(i_1\) and \(i_2\).

variance([operator, tol])

Compute the variance on input operator.

Attributes

evals

Eigenvalues in ascending order.

evecs

Eigenvectors in the order accordingly to evals.

matrix

n_sites

phys_dim

proj

__init__(mpo, proj=None)[source]#

Perform the numerically exact diagonalization on the matrix, which is constructed through the given Matrix Product Operator (MPO). Calculations are taken in prompt on the initialization of this class.

Parameters
Raises

ResourceWarning – When the dimensions of Hamiltonian are larger than \(4096 \times 4096\).

Examples

>>> ed = ExactDiagonalization(mpo)
>>> evals = ed.evals
>>> evecs = ed.evecs
property proj: numpy.ndarray#
property evals: numpy.ndarray#

Eigenvalues in ascending order.

property evecs: numpy.ndarray#

Eigenvectors in the order accordingly to evals.

Returns

The eigenvectors, with the column v[:, k] is the eigenvector corresponding to the k-th eigenvalue w[k].

reduced_density_matrix(site, level_idx=0)[source]#

Compute the reduced density matrix on the bi-partition site \(i\) through the singular value decomposition.

\[\rho_A = tr_B \rho\]
Parameters

  • site (int) – The site to which the bi-partition is taken on the bond \(i\) to \(i+1\).

  • level_idx (int) – Compute on k-th eigenvector. Default 0 to the 1st eigenvector.

Return type

numpy.ndarray

Returns:

entanglement_entropy(site, level_idx=0, nan_to_num=False)[source]#

Compute the von Neumann entropy on the cutting site.

Parameters

  • site (int) – The site to which the bi-partition is taken on the bond \(i\) to \(i+1\).

  • level_idx (int) – Compute on k-th eigenvector. Default 0 to the 1st eigenvector.

  • nan_to_num (bool) – If True, convert NaN to zero. Default False.

Return type

float

Returns:

static kron_operators(operators)[source]#

Perform Kronecker product on the given sequence of operators. This can be used to construct, for instance, \(I_1 \otimes \cdots \otimes S_i^z \otimes \cdots \otimes I_N\) on the many-body basis.

Parameters

operators (Sequence[numpy.ndarray]) – A list of operators to take Kronecker product.

Returns

The resulting product operator.

Return type

numpy.ndarray

one_point_function(operator, site, level_idx=0)[source]#

Compute the expectation value \(\langle \hat{O}_i \rangle\) of given local operator \(\hat{O}_i\) on site \(i\).

Parameters

  • operator (numpy.ndarray) – The operator \(\hat{O}\).

  • site (int) –

  • level_idx (int) –

Return type

float

Returns:

two_point_function(operator1, operator2, site1, site2, level_idx)[source]#

Compute the correlation function \(\langle \hat{O}_{i_1}^A \hat{O}_{i_2}^B \rangle\) of 2 given local operators \(\hat{O}_{i_1}^A\) and \(\hat{O}_{i_2}^B\) on site \(i_1\) and \(i_2\).

Parameters

  • operator1 (numpy.ndarray) – The first operator \(\hat{O}^A\).

  • operator2 (numpy.ndarray) – The second operator \(\hat{O}^B\).

  • site1 (int) –

  • site2 (int) –

  • level_idx (int) –

Return type

float

Returns:

connected_two_point_function(operator1, operator2, site1, site2, level_idx)[source]#
Parameters
Return type

float

Returns:

variance(operator=None, tol=1e-12)[source]#

Compute the variance on input operator.

Parameters

  • operator (Optional[numpy.ndarray]) – Default None to the Hamailtonian itself.

  • tol (float) – The numerical tolerance.

Returns

The variance.

Raises

Warnings – If any off-diagonal element is larger than tol.

Return type

numpy.ndarray