Exploring the Entanglement Spectrum of the 2-D Chern Insulator

Abstract

The entanglement Hamiltonian is a dimensionless quantity that allows us to probe topological features within the bulk of a system by focusing on a specific subsystem and tracing out unwanted degrees of freedom. The entanglement spectrum has a particularly nice decomposition into two point correlation functions in the free-fermion model, a formalism we apply to the 2-D Chern Insulator. We first provide a generic qualitative description of the entanglement/correlation spectra at zero and finite temperature. We then explore the behavior of the entanglement and correlation spectra as we approach the topological critical point. We observe finite-size and finite temperature effects, and try to explain their impact by relating the entanglement/correlation spectra back to the physical spectrum. We also analytically solve for the entanglement eigenstates in the zero-temperature case and discuss the subtleties involved in picking proper boundary conditions.