Scaling behavior and phase diagram of a PT-symmetric non-Hermitian Bose-Hubbard system

TL;DR

This paper investigates the scaling behavior and phase diagram of a PT-symmetric non-Hermitian Bose-Hubbard model, revealing how interactions influence PT symmetry and the structure of phase transitions.

Contribution

It provides a comprehensive analysis of the metric operator, similarity matrix, and phase diagram, highlighting the effects of interactions on PT symmetry breaking and exceptional points.

Findings

Diverging derivatives near exceptional points indicate dramatic matrix element changes.

Small on-site interactions can significantly break PT symmetry.

Multiple regions of unbroken PT symmetry are identified in the phase diagram.

Abstract

We study scaling behavior and phase diagram of a PT-symmetric non-Hermitian Bose-Hubbard model. In the free interaction case, using both analytical and numerical approaches, the metric operator for many-particle is constructed. The derived properties of the metric operator, similarity matrix and equivalent Hamiltonian reflect the fact that all the matrix elements change dramatically with diverging derivatives near the exceptional point. In the nonzero interaction case, it is found that even small on-site interaction can break the PT symmetry drastically. It is demonstrated that the scaling law can be established for the exceptional point in both small and large interaction limit. Based on perturbation and numerical methods, we also find that the phase diagram shows rich structure: there exist multiple regions of unbroken PT symmetry.