quspin.tools.misc.project_op

quspin.tools.misc.project_op(Obs, proj, dtype=<class 'numpy.complex128'>)[source]

Projects observable onto symmetry-reduced subspace.

This function takes an observable Obs and a reduced basis or a projector proj, and projects Obs onto that reduced basis.

Parameters:

Obs:obj:

Operator to be projected, either a numpy.ndarray or a hamiltonian object.

proj:obj:

Either one of the following:

• basis object with the basis of the Hilbert space after the projection.

• numpy.ndarray: a matrix which contains the projector.

Projectors can be calculated conveniently using the function method basis.get_proj().

dtypetype, optional

Data type of output. Default is numpy.complex128.

Returns:

dict

Dictionary with keys

• “Proj_Obs”: projected observable Obs.

Examples

The following example shows how to project an operator \(H_1=\sum_j hS^x_j + g S^z_j\) from the symmetry-reduced basis to the full basis.

 1from quspin.basis import spin_basis_1d  # Hilbert space spin basis
 2from quspin.tools.measurements import project_op
 3import numpy as np  # generic math functions
 4
 5#
 6L = 12  # syste size
 7# coupling strenghts
 8h = 0.8945  # x-field strength
 9g = 0.945  # z-field strength
10# create site-coupling lists
11x_field = [[h, i] for i in range(L)]
12z_field = [[g, i] for i in range(L)]
13# create static and dynamic lists
14static_1 = [["x", x_field], ["z", z_field]]
15dynamic = []
16# create spin-1/2 basis
17basis = spin_basis_1d(L, kblock=0, pblock=1)
18# set up Hamiltonian
19H1 = hamiltonian(static_1, dynamic, basis=basis, dtype=np.float64)
20# compute eigensystem of H1
21E1, V1 = H1.eigh()
22psi1 = V1[:, 14]  # pick any state as initial state
23#
24# project Hamiltonian from `kblock=0` and `pblock=1` onto full Hilbert space
25proj = basis.get_proj(np.float64)  # calculate projector
26H1_full = project_op(H1, proj, dtype=np.float64)["Proj_Obs"]
27print(
28    "dimenions of symmetry-reduced and full Hilbert spaces are %i and %i."
29    % (H1.Ns, H1_full.Ns)
30)