Extracting subleading corrections in entanglement entropy at quantum phase transitions

TL;DR

This paper analyzes the finite size scaling of entanglement entropy in 2D quantum systems near phase transitions, revealing subleading corrections linked to Goldstone modes and quantum critical points.

Contribution

It systematically investigates subleading entanglement entropy corrections across various 2D quantum models, clarifying their relation to boundary features and critical phenomena.

Findings

Logarithmic correction consistent with Goldstone modes in Neel order.

Absence of logarithmic correction in smooth boundary at 2+1D O(3) critical point.

Logarithmic correction present in deconfined quantum critical points with smooth boundary.

Abstract

We systematically investigate the finite size scaling behavior of the R\'enyi entanglement entropy (EE) of several representative 2d quantum many-body systems between a subregion and its complement, with smooth boundaries as well as boundaries with corners. In order to reveal the subleading correction, we investigate the quantity ``subtracted EE" $S^s(l) = S(2l) - 2S(l)$ for each model, which is designed to cancel out the leading perimeter law. We find that $\mathbf{(1)}$ for a spin-1/2 model on a 2d square lattice whose ground state is the Neel order, the coefficient of the logarithmic correction to the perimeter law is consistent with the prediction based on the Goldstone modes; $\mathbf{(2)}$ for the $(2+1)d$ O(3) Wilson-Fisher quantum critical point (QCP), realized with the bilayer antiferromagnetic Heisenberg model, a logarithmic subleading correction exists when there is sharp corner of the subregion, but for subregion with a smooth boundary our data suggests the absence of the logarithmic correction to the best of our efforts; $\mathbf{(3)}$ for the $(2+1)d$ SU(2) J-Q$_2$ and J-Q$_3$ model for the deconfined quantum critical point (DQCP), we find a logarithmic correction for the EE even with smooth boundary.