Entanglement used to identify critical systems

Abstract

We promote use of the geometric entropy formula derived by Holzhey et. al. from conformal field theory, $S_{\ell }\sim (c/3)\log (\sin \pi \ell /N)$, to identify critical regions in zero temperature 1D quantum systems. The method is demonstrated on a class of one-dimensional XY and $XYZ$ spin-1/2 chains, where the critical regions and their correponding central charges can be reproduced with quite modest computational efforts.

4 pages, 7 figures