Finite Size Corrections to Entanglement in Quantum Critical Systems

TL;DR

This paper investigates how finite system size affects entanglement in quantum critical systems, revealing universal patterns governed by conformal symmetry and the central charge, with applications to spin chains.

Contribution

It introduces a universal framework for understanding finite size corrections to entanglement using conformal field theory and density functional theory.

Findings

Finite size corrections are governed by the central charge of the conformal field theory.

Entanglement patterns in excited states follow a universal structure related to primary operator dimensions.

Application to the XXZ spin chain illustrates the theoretical predictions.

Abstract

We analyze the finite size corrections to entanglement in quantum critical systems. By using conformal symmetry and density functional theory, we discuss the structure of the finite size contributions to a general measure of ground state entanglement, which are ruled by the central charge of the underlying conformal field theory. More generally, we show that all conformal towers formed by an infinite number of excited states (as the size of the system $L \to \infty$) exhibit a unique pattern of entanglement, which differ only at leading order $(1/L)^2$. In this case, entanglement is also shown to obey a universal structure, given by the anomalous dimensions of the primary operators of the theory. As an illustration, we discuss the behavior of pairwise entanglement for the eigenspectrum of the spin-1/2 XXZ chain with an arbitrary length $L$ for both periodic and twisted boundary conditions.