Entanglement Chern Number of the Kane-Mele Model with Ferromagnetism

TL;DR

This paper uses the entanglement Chern number to analyze the Kane-Mele model, including cases with broken time reversal symmetry and spin conservation, revealing a relationship between entanglement and traditional Chern numbers.

Contribution

It introduces the entanglement Chern number as a tool to characterize the Kane-Mele model and extends its application to non-symmetric cases with Zeeman terms.

Findings

The entanglement Chern number characterizes the quantum spin Hall phase.

The sum of entanglement spin Chern numbers equals the Chern number.

The method remains effective without time reversal symmetry or spin conservation.

Abstract

The entanglement Chern number, the Chern number for the entanglement Hamiltonian, is used to charac- terize the Kane-Mele model, which is a typical model of the quantum spin Hall phase with the time reversal symmetry. We first obtain the global phase diagram of the Kane-Mele model in terms of the entanglement spin Chern number, which is defined by using a spin subspace as a subspace to be traced out in preparing the entanglement Hamiltonian. We further demonstrate the effectiveness of the entanglement Chern number without the time reversal symmetry and spin conservation by extending the Kane-Mele model to include the Zeeman term. The numerical results confirm that the sum of the entanglement spin Chern number equals to the Chern number.