Entanglement used to identify critical systems

TL;DR

This paper demonstrates how geometric entropy can be used to identify critical regions in 1D quantum systems, effectively determining phase transitions with minimal computational resources.

Contribution

It applies the conformal field theory-derived geometric entropy formula to detect criticality in 1D spin chains, showing practical utility and efficiency.

Findings

Successfully identified critical regions in XY and XYZ spin chains.

Reproduced central charges with modest computational effort.

Validated the geometric entropy approach as a practical tool for quantum criticality detection.

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.