Numerical calculation of the complex berry phase in non-Hermitian systems

TL;DR

This paper develops a numerical method to calculate complex Berry phases in non-Hermitian, dissipative lattice systems, enabling better understanding of their topological properties.

Contribution

A general numerical gauge smoothing procedure for calculating complex Berry phases in non-Hermitian systems is introduced and validated.

Findings

Successfully applied to a 1D $ ext{PT}$-symmetric lattice system

Validated numerical results with analytical calculations

Provides insights into topological phases under dissipation

Abstract

We numerically investigate topological phases of periodic lattice systems in tight-binding description under the influence of dissipation. The effects of dissipation are effectively described by $\mathcal{PT}$-symmetric potentials. In this framework we develop a general numerical gauge smoothing procedure to calculate complex Berry phases from the biorthogonal basis of the system's non-Hermitian Hamiltonian. Further, we apply this method to a one-dimensional $\mathcal{PT}$-symmetric lattice system and verify our numerical results by an analytical calculation.