Entanglement Spectrum and Entanglement Hamiltonian of a Chern insulator with open boundaries

TL;DR

This paper investigates the entanglement spectrum of a Chern insulator on a cylinder, revealing how edge localization affects the entanglement gap and constructing the associated entanglement Hamiltonian with complex long-range hopping.

Contribution

It provides a detailed analysis of the entanglement spectrum with open boundaries and constructs the entanglement Hamiltonian for a single-row cut, highlighting the effects of edge localization.

Findings

Entanglement spectrum gap depends on edge mode localization.

Perfectly localized edge modes lead to a gapless entanglement spectrum.

Constructed a 1D entanglement Hamiltonian with complex long-range hopping.

Abstract

We study the entanglement spectrum of a Chern insulator on a cylinder geometry, with the cut separating the two partitions taken parallel to the cylinder edge, at varying distances from the edge. In contrast to similar studies on a torus, there is only one cut, and hence only one virtual edge mode in the entanglement spectrum. The entanglement spectrum has a gap when the cut is close enough to the physical edge of the cylinder such that the edge mode spatially extends over the cut. This effect is suppressed for parameter choices where the edge mode is sharply localized at the edge. In the extreme case of a perfectly localized edge mode, the entanglement spectrum is gapless even if the smaller partition consists of a single edge row. For the single-row cut, we construct the corresponding entanglement Hamiltonian, which is a one-dimensional tight-binding Hamiltonian with complex long-range hopping and interesting properties. We also study and explain the effect of two different schemes of flux insertion through a ring described by such an entanglement Hamiltonian.