4.4. tnpy.tsdrg.TreeTensorNetworkMeasurements#

class tnpy.tsdrg.TreeTensorNetworkMeasurements(tree)[source]#

Bases: object

A collection of all available physical measurements for TensorTree.

Parameters

tree (TensorTree) – The renormalized eigenstates in tree representation.

__init__(tree)[source]#

A collection of all available physical measurements for TensorTree.

Parameters

tree (tnpy.tsdrg.TensorTree) – The renormalized eigenstates in tree representation.

Methods

__init__(tree)

A collection of all available physical measurements for TensorTree.

connected_two_point_function(operator1, ...)

param operator1

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

Compute the von Neumann entropy on the cutting site.

expectation_value(mpo[, tol])

Compute the expectation value for given mpo.

kullback_leibler_divergence()

loop_simplify(bra, ket[, mpo])

Simplify every closed loop within the network bra & mpo & ket.

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 \(i\).

participation_entropy()

reduced_density_matrix(site, level_idx)

Compute the reduced density matrix for the bipartite system with respect to the cutting site.

sandwich([mpo])

Take the sandwich on given mpo.

squared_moduli(level_idx)

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(mpo)

Compute the variance on given matrix product operator.

wave_func_coeff(level_idx)

Attributes

tree

__init__(tree)[source]#

A collection of all available physical measurements for TensorTree.

Parameters

tree (tnpy.tsdrg.TensorTree) – The renormalized eigenstates in tree representation.

property tree: tnpy.tsdrg.TensorTree#
loop_simplify(bra, ket, mpo=None)[source]#

Simplify every closed loop within the network bra & mpo & ket.

Parameters

  • bra (quimb.tensor.tensor_core.TensorNetwork) – Tree tensor network which represents the bra vector.

  • ket (quimb.tensor.tensor_core.TensorNetwork) – Tree tensor network which represents the ket vector.

  • mpo (Optional[tnpy.operators.MatrixProductOperator]) – (Optional) If not given, bra & ket will be computed.

Returns

The contracted tensor.

Return type

quimb.tensor.tensor_core.Tensor

Notes

quimb may provide other simplify methods based on greedy algorithm.

sandwich(mpo=None)[source]#

Take the sandwich on given mpo. If it is None, this computes the inner product of state.

Parameters

mpo (Optional[tnpy.operators.MatrixProductOperator]) –

Return type

quimb.tensor.tensor_core.Tensor

Returns:

expectation_value(mpo, tol=1e-12)[source]#

Compute the expectation value for given mpo.

Parameters
Returns

The expectation values.

Raises

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

Return type

numpy.ndarray

reduced_density_matrix(site, level_idx)[source]#

Compute the reduced density matrix for the bipartite system with respect to the cutting site.

Parameters

  • site (int) –

  • level_idx (int) –

Return type

numpy.ndarray

Returns:

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

Compute the von Neumann entropy on the cutting site.

Parameters

  • site (int) –

  • level_idx (int) –

  • nan_to_num (bool) –

Return type

float

Returns:

one_point_function(operator, site, level_idx)[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(mpo)[source]#

Compute the variance on given matrix product operator.

Parameters

mpo (tnpy.operators.MatrixProductOperator) – The matrix product operator.

Returns

The variance.

Return type

numpy.ndarray

wave_func_coeff(level_idx)[source]#
Parameters

level_idx (int) –

squared_moduli(level_idx)[source]#
Parameters

level_idx (int) –

kullback_leibler_divergence()[source]#
participation_entropy()[source]#