Entanglement Spectrum of a Disordered Topological Chern Insulator

TL;DR

This paper investigates how the entanglement spectrum of a disordered topological Chern insulator encodes information about its phase, using statistical analysis to distinguish topological from trivial phases without relying on symmetry.

Contribution

It introduces a method to analyze the entanglement spectrum of disordered systems without symmetry, using level statistics to identify topological phases and phase boundaries.

Findings

Level statistics of the entanglement spectrum can distinguish topological from trivial phases.

The phase diagram is mapped as a function of Fermi level and disorder strength.

The Chern number is computed using an efficient real-space formula.

Abstract

How much information is stored in the ground-state of a system without \emph{any symmetry} and how can we extract it? This question is investigated by analyzing the behavior of a topological Chern Insulator (CI) in the presence of disorder, with a focus on its entanglement spectrum (EtS) constructed from the ground state. For systems with symmetries, the EtS was shown to contain explicit information revealed by sorting the EtS against the conserved quantum numbers. In the absence of any symmetry, we demonstrate that statistical methods such as the level statistics of the EtS can be equally insightful, allowing us to distinguish when an insulator is in a topological or trivial phase and to map the boundary between the two phases, where EtS becomes entirely delocalized. The phase diagram of a CI is explicitly computed as function of Fermi level ($E_F$) and disorder strength using the level statistics of the EtS and energy spectrum (EnS), together with a computation of the Chern number via an efficient real-space formula.