On the eigenvalues of some non-Hermitian Hamiltonians with space-time symmetry

TL;DR

This paper computes eigenvalues of certain non-Hermitian Hamiltonians using pseudospectral and diagonalization methods, finding results that differ from previous studies and challenging earlier claims of multiple phase transitions.

Contribution

It introduces a pseudospectral approach for eigenvalue calculation and provides new insights that contradict earlier findings on phase transitions in these systems.

Findings

Results agree well between methods but differ from previous studies.

No evidence of multiple phase transitions in the examined anharmonic oscillator.

Eigenvalues are reliably computed using the combined numerical approaches.

Abstract

We calculate the eigenvalues of some two-dimensional non-Hermitian Hamiltonians by means of a pseudospectral method and straightforward diagonalization of the Hamiltonian matrix in a suitable basis set. Both sets of results agree remarkably well but differ considerably from the eigenvalues obtained some time ago by other authors. In particular, we do not observe the multiple phase transitions claimed to occur in one of the anharmonic oscillators.