The scaling of entanglement entropy in a honeycomb lattice on a torus

TL;DR

This paper investigates how entanglement entropy behaves in a two-dimensional honeycomb lattice of noninteracting fermions on a torus, revealing its ability to characterize Lifshitz phase transitions and its scaling properties.

Contribution

It provides a detailed analysis of entanglement entropy scaling in a honeycomb lattice, highlighting its role in identifying phase transitions without local order parameters.

Findings

Entanglement entropy follows an area law in both gapped and critical phases.

The subarea term is constant in gapped phases and logarithmically violated in gapless phases.

Numerical and analytical results are in agreement, and entanglement spectrum relates to edge spectrum.

Abstract

The entanglement entropy of a noninteracting fermionic system confined to a two-dimensional honeycomb lattice on a torus is calculated. We find that the entanglement entropy can characterize Lifshitz phase transitions without a local order parameter. In the noncritical phase and critical phase with a nodal Fermi surface, the entanglement entropy satisfies an area law. The leading subarea term is a constant in the gapped phase rather than a logarithmic additive term in the gapless regime. The tuning of chemical potential allows for a nonzero Fermi surface, whose variation along a particular direction determines a logarithmic violation of the area law. We perform the scaling of entanglement entropy numerically and find agreement between the analytic and numerical results. Furthermore, we clearly show that an entanglement spectrum is equivalent to an edge spectrum.