Entanglement entropy of random partitioning

TL;DR

This paper investigates how entanglement entropy behaves in critical fermionic systems with randomly chosen partitions, revealing volume and boundary scaling with universal and non-universal components, and highlighting differences across dimensions.

Contribution

It provides a detailed analysis of entanglement entropy scaling in random partitions of critical fermionic systems, including universal functions and percolation effects in 2D.

Findings

Entanglement entropy scales with volume and boundary terms, including logarithmic corrections.

In 1D, the boundary prefactor relates to the central charge and a universal function.

In 2D, the prefactor varies with percolation threshold, indicating phase-dependent behavior.

Abstract

We study the entanglement entropy of random partitions in one- and two-dimensional critical fermionic systems. In an infinite system we consider a finite, connected (hypercubic) domain of linear extent $L$, the points of which with probability $p$ belong to the subsystem. The leading contribution to the average entanglement entropy is found to scale with the volume as $a(p) L^D$, where $a(p)$ is a non-universal function, to which there is a logarithmic correction term, $b(p)L^{D-1}\ln L$. In $1D$ the prefactor is given by $b(p)=\frac{c}{3} f(p)$, where $c$ is the central charge of the model and $f(p)$ is a universal function. In $2D$ the prefactor has a different functional form of $p$ below and above the percolation threshold.