Two-spin correlator with quantum_LinearOperator

Quspin 0.3.0, Anaconda 64bit Windows, Python 3.6

Problem statement

I would like to create a two-spin correlator operator for calculating spin-spin correlations in a 1D Ising chain (simplest possible case) with nearest neighbour interactions only. (I know I can use classical spins ±1, but eventually I need to use this for quantum spins as well in more complicated lattice structure).

Suppose L = 6, the spin chain (periodic bc) looks like

- 0 - 1 - 2 - 3 - 4 - 5 -

and the following MWE:

from quspin.operators import hamiltonian, quantum_LinearOperator
from quspin.basis import spin_basis_1d
import numpy as np

NN_PAIRS = [(0, 1), (1, 2), (2, 3), (3, 4), (4, 5), (5, 0)]
Jzz = [[1, i, j] for (i, j) in NN_PAIRS]  # NN only, with pbc
static = [["zz", Jzz]]
basis = spin_basis_1d(6, S='1/2', pauli=True)
H = hamiltonian(static, [], basis=basis)
eigvals, eigvecs = H.eigh()

uu_coeff = [[1.0, 0, 4]]  # want <s0 s4>
uu_op = quantum_LinearOperator(static_list=[['zz', uu_coeff]], basis=basis,
                               check_herm=False, check_symm=False)

# Below, for context only
ss_avg, Z = 0., 0.
kT = 0.04309

# shift eigenvalue spectrum to avoid negative E and large Z values; leaves thermal avg unchanged
eigvals -= eigvals.min()

for E_n, n in zip(eigvals, eigvecs):
    ss_avg += np.dot(n.conj(), uu_op.matvec(n)) * np.exp(-E_n / kT)
    Z += np.exp(-E_n / kT)

print(ss_avg/Z)

For context: I’m generating uu_op in order to calculate, for example, the (real-space) spin-spin correlation between spin 0 and spin 4, using the thermal average (n and E_n are eigenvecs and eigenvals of H respectively):

If my physics is right, this shouldn’t give 0 at the end (if you run my MWE).

---

So something’s clearly wrong, but first a question related to Quspin’s functionality:

I was inspecting the uu_op (i.e., of the quantum_LinearOperator module) object properties and realized its static_list is empty. Am I doing something wrong? I would’ve expected the static list would contain the list I passed in (uu_coeff in MWE above), but it does not (see pic below). Whereas, the Hamiltonian H contains the static list just fine.

(uu_op.static_list.__len__ = 0)

[mgbukov]

Hi thatlittleboy,

I had a look at your QuSpin code, it seems fine to me.

1. I think quantum_LinearOperator actually gives the correct result: to check this, I used hamiltonian to define the operator $s_0 s^4$, as follows:

uu_op = hamiltonian([['zz', uu_coeff]],[], basis=basis, check_herm=False, check_symm=False)

You should also modify the line where you compute the expectation value in the loop to

ss_avg += uu_op.expt_value(n) * np.exp(-E_n / kT)

This produces the same result, which suggests that QuSpin is doing fine.

1. I then looked up your for-loop, and noticed that the zip function is looping over the wrong axis of eigvecs. If you instead do

for E_n, n in zip(eigvals, eigvecs.T):

everything works fine 😉

@ Phil:

i) indeed the static_list attribute is empty. I looked up the quantum_LinearOperator source code, and static_list should be declared within the scope of the if statement in line 131 but it’s not. I would’ve put it in myself, but I don’t really get the meaning of this else part of the statement (it seems completely unrelated to the if-part). Can u have a look and maybe fix this in the dev branch?

ii) just noticed that in the online documentation, quantum_LinearOperator is missing its class example. There was a typo with one of the letters being lowercase in the sphinx source code. I just fixed it and pushed this into dev_0.3.1 branch, but we may need to update the online doc right away for the benefit of the users?

– marin

[mgbukov]

this is fixed in v. 0.3.1