Regular Article

Entanglement entropy of random partitioning^★

¹ Institute of Theoretical Physics, Technische Universität Dresden, 01062 Dresden, Germany
² Wigner Research Centre for Physics, Institute for Solid State Physics and Optics, P.O. Box 49, 1525 Budapest, Hungary
³ Department of Physics and Astronomy, Northwestern University, Evanston, IL 60208-3112, USA
⁴ Department of Network and Data Science, Central European University, Budapest 1051, Hungary
⁵ Institute of Theoretical Physics, Szeged University, 6720 Szeged, Hungary

^a e-mail: gergoe.roosz@tu-dresden.de

Received: 11 October 2019
Received in final form: 21 November 2019
Published online: 20 January 2020

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)=c/3f(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.