Bounds on corner entanglement in quantum critical states

TL;DR

This paper investigates the universal properties of corner contributions to entanglement entropy in 2+1d quantum critical states, deriving bounds and uncovering new information beyond stress tensor correlators.

Contribution

It establishes bounds on corner entanglement functions, relates higher-order terms to four-point stress tensor data, and provides exact results for various quantum critical models.

Findings

Lower bound on $a( heta)$ in terms of $C_T$

Nearly saturated bound at 90-degree corners for known models

Exact results for Lifshitz and conical singularities

Abstract

The entanglement entropy in many gapless quantum systems receives a contribution from corners in the entangling surface in 2+1d. It is characterized by a universal function $a(\theta)$ depending on the opening angle $\theta$, and contains pertinent low energy information. For conformal field theories (CFTs), the leading expansion coefficient in the smooth limit $\theta \to \pi$ yields the stress tensor 2-point function coefficient $C_T$ . Little is known about $a(\theta)$ beyond that limit. Here, we show that the next term in the smooth limit expansion contains information beyond the 2- and 3-point correlators of the stress tensor. We conjecture that it encodes 4-point data, making it much richer. Further, we establish strong constraints on this and higher order smooth-limit coefficients. We also show that $a(\theta)$ is lower-bounded by a non-trivial function multiplied by the central charge $C_T$ , e.g. $a(\pi/2) \geq (\pi^2 \ln 2)C_T /6$. This bound for 90-degree corners is nearly saturated by all known results, including recent numerics for the interacting Wilson-Fisher quantum critical points (QCPs). A bound is also given for the R\'enyi entropies. We illustrate our findings using O(N) QCPs, free boson and Dirac fermion CFTs, strongly coupled holographic ones, and other models. Exact results are also given for Lifshitz quantum critical points, and for conical singularities in 3+1d.