Universal corner entanglement of Dirac fermions and gapless bosons from the continuum to the lattice

TL;DR

This paper investigates the universal corner contributions to entanglement entropy in two-dimensional quantum critical systems, providing high-precision lattice results, theoretical estimates, and bounds for free and interacting conformal field theories.

Contribution

It offers the first comprehensive numerical and theoretical analysis of the corner entanglement coefficient $a_eta( heta)$ for Dirac fermions and bosons, including new exact results and bounds.

Findings

Excellent agreement between numerical and theoretical results for $a_eta( heta)$

Derived new exact results for corner entanglement coefficients

Established strong lower bounds applicable to various quantum critical systems

Abstract

A quantum critical (QC) fluid exhibits universal subleading corrections to the area law of its entanglement entropies. In two dimensions when the partition involves a corner of angle $\theta$, the subleading term is logarithmic with coefficient $a_\alpha(\theta)$ for the $\alpha$-R\'enyi entropy. In the smooth limit $\theta\!\to\!\pi$, $a_1(\theta)$ yields the central charge of the stress tensor when the QC point is described by a conformal field theory (CFT). For general R\'enyi indices and angles, $a_\alpha(\theta)$ is richer and few general results exist. We study $a_\alpha(\theta)$ focusing on two benchmark CFTs, the free Dirac fermion and boson. We perform numerical lattice calculations to obtain high precision results in $\theta,\alpha$ regimes hitherto unexplored. We derive field theory estimates for $a_\alpha(\theta)$, including new exact results, and demonstrate an excellent quantitative match with our numerical calculations. We also develop and test strong lower bounds, which apply to both free and interacting QC systems. Finally, we comment on the near collapse of $a_\alpha(\theta)$ for various theories, including interacting $O(N)$ models.