Tool for evaluating the polar-decomposition WPD invariant for finite one-dimensional non-Hermitian chains. This tool is based on the principle introduced in arXiv:2607.05900.

The input is a square NumPy array containing the finite-chain Hamiltonian. The saved RF model predicts the crop length ell_star, and the WPD invariant is then evaluated directly from the supplied matrix.

This folder contains: -nhwpd.py -README.md

Download model.zip from the Zenodo archive linked below and extract the model.pkl file into the same folder as nhwpd.py.

Zenodo model file: https://zenodo.org/records/21338187

How to use: (Example)

import numpy as np
from nhwpd import evaluate_wpd

# Suppose you want to evaluate the invariant for the Hamiltonian matrix 
# of an N-site Hatano-Nelson chain.
N = 128
H = np.zeros((N, N), dtype=complex)
for n in range(N - 1):
    H[n + 1, n] = 1.0
    H[n, n + 1] = 0.55

# Assuming the model.pkl file is in the same folder
result = evaluate_wpd(H, E_B=0.0)

For evaluating the invariant directly for a matrix, load the matrix and use the tool as:

H = np.load("matrix.npy")
result = evaluate_wpd(H, E_B=0.0)

If the matrix is disordered, the script first averages each hopping diagonal and feeds that effective finite-range clean model to the RF predictor. This predicts a crop-length ell_star which is used to evaluate the wpd invariant for the original disordered input matrix. The code also computes the winding number of the diagonal-averaged clean matrix. "distance_to_clean_winding" and "reliable" say whether the wpd value is close to this clean winding.

The default tolerance is 0.1. If the predicted ell_star does not give a wpd close to the clean winding, the code tries larger crop lengths in steps of 5 until the tolerance is reached or no larger crop is possible.

If no available crop reaches the tolerance, evaluate_wpd raises MatrixTooSmallError. This usually means that the matrix is too small for this base energy and tolerance.

The diagonal averaging is only a guide for selecting ell_star. If a matrix has isolated large entries, or otherwise is not well represented by averaged diagonals, the predicted crop length may be unreliable. In that case result["residual"] will usually be large.