Thermodynamic singularities in the entanglement entropy at a 2D quantum critical point

TL;DR

This paper investigates the behavior of entanglement entropy in a 2D quantum critical system, revealing unique singularities at corners and demonstrating the effectiveness of series expansion methods for interacting quantum systems.

Contribution

The study introduces series expansion techniques to analyze entanglement entropy near quantum critical points in 2D, highlighting differences from free field theories.

Findings

Entanglement at corners exhibits distinct singularities from free boson theories.

Series expansions accurately match known results in 1D and reveal new insights in 2D.

Corner entanglement shows significant deviations from simple theoretical models.

Abstract

We study the bipartite entanglement entropy of the two-dimensional (2D) transverse-field Ising model in the thermodynamic limit using series expansion methods. Expansions are developed for the Renyi entropy around both the small-field and large-field limits, allowing the separate calculation of the entanglement associated with lines and corners at the boundary between sub-systems. Series extrapolations are used to extract subleading power laws and logarithmic singularities as the quantum critical point is approached. In 1D, we find excellent agreement with exact results as well as quantum Monte Carlo simulations. In 2D, we find compelling evidence that the entanglement at a corner is significantly different from a free boson field theory. These results demonstrate the power of the series expansion method for calculating entanglement entropy in interacting systems, a fact that will be particularly useful in future searches for exotic quantum criticality in models with and without the sign problem.