Polarization and entanglement spectrum in non-hermitian systems

TL;DR

This paper investigates the properties of entanglement spectra in non-Hermitian systems, revealing how they encode topological information, polarization, and phase diagrams, with distinctions between point-gapped and line-gapped phases.

Contribution

It provides a detailed analysis of entanglement spectra in non-Hermitian systems, highlighting their ability to reflect topological features and polarization, and establishing the equivalence of Wilson loop and many-body polarization.

Findings

Entanglement spectrum captures topological edge modes in line-gapped phases.

In non-Hermitian systems, the entanglement spectrum encodes polarization even without topological order.

Wilson loop reproduces phase diagrams for open boundary conditions from periodic systems.

Abstract

The entanglement spectrum is a useful tool to study topological phases of matter, and contains valuable information about the ground state of the system. Here, we study its properties for free non-Hermitian systems for both point-gapped and line-gapped phases. While the entanglement spectrum only retains part of the topological information in the former case, it is very similar to Hermitian systems in the latter. In particular, it not only mimics the topological edge modes, but also contains all the information about the polarization, even in systems that are not topological. Furthermore, we show that the Wilson loop is equivalent to the many-body polarization and that it reproduces the phase diagram for the system with open boundaries, despite being computed for a periodic system.