Bath Construction Fails for Coupling Ops with Degenerate Eigenvalues

[sergleonov]

Constructing an oqupy.Bath raises an AssertionError (line 77 in bath.py) when the system–bath coupling operator is Hermitian but has a 3 degenerate non-zero eigenvalues. Failing check is the following attempt to reconstruct the original matrix:

assert np.allclose(
    tmp_coupling_operator, self._unitary @ self._coupling_operator @ self._unitary.conjugate().T,
)

Currently, the coupling operator is diagonalised with a non-Hermitian eigensolver, which does not return an orthonormal eigenbasis within degenerate eigenspaces. As a result, U @ diag @ U† no longer reconstructs the original operator. Diagonalising with a Hermitian eigensolver (numpy.linalg.eigh) fixes it.

Minimal example

import numpy as np
import oqupy
def collective_sigma_x(n):
    # construct tensor product of sigma X operators for 3 TLSs
    sx = oqupy.operators.sigma("x")
    I = np.identity(2)
    total = np.zeros((2 ** n, 2 ** n), dtype=complex)
    for i in range(n):
        ops = [I for _ in range(n)]
        ops[i] = sx
        term = ops[0]
        for op in ops[1:]:
            term = np.kron(term, op)
        total += term
    return total
correlations = oqupy.PowerLawSD(

alpha=0.02, zeta=1, cutoff=0.5,

cutoff_type="exponential", temperature=0.5,

)
oqupy.Bath(collective_sigma_x(2), correlations) # works

oqupy.Bath(collective_sigma_x(3), correlations) # breaks, but can be fixed with eigh()

Environment

• oqupy 0.5.0
• numpy 2.x
• Python 3.11

[piperfw]

Hi @sergleonov, thanks for providing an example and a recommended fix! As we already check for Hermiticity of the bath operator, I believe using eigh here is a safe and reliable option. We should get that fixed in main soon (see #166)

[sergleonov]

Thank you very much!