Entanglement Spectrum of a Disordered Topological Chern Insulator

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.