A chain of solvable non-Hermitian Hamiltonians constructed by a series of metric operators

TL;DR

This paper introduces a method to generate an infinite chain of isospectral non-Hermitian Hamiltonians from a given one, using a series of metric operators, simplifying the analysis of such systems.

Contribution

The authors develop a novel iterative procedure to construct multiple non-Hermitian Hamiltonians linked by metric operators, expanding the toolkit for analyzing non-Hermitian quantum systems.

Findings

Successfully applied to Hatano-Nelson models

Extended to PT-symmetric Hamiltonians

Provides an almost automatic eigenvector deduction method

Abstract

We show how, given a non-Hermitian Hamiltonian $H$, we can generate new non-Hermitian operators sequentially, producing a virtually infinite chain of non-Hermitian Hamiltonians which are isospectral to $H$ and $H^\dagger$ and whose eigenvectors we can easily deduce in an almost automatic way; no ingredients are necessary other than $H$ and its eigensystem. To set off the chain and keep it running, we use, for the first time in our knowledge, a series of maps all connected to different metric operators. We show how the procedure works in several physically relevant systems. In particular, we apply our method to various versions of the Hatano-Nelson model and to some PT-symmetric Hamiltonians.