Bell Function Values Approach to Topological Quantum Phase Transitions

TL;DR

This paper demonstrates that Bell function values can effectively identify topological quantum phase transitions in the Kitaev-Castelnovo-Chamon model, linking quantum nonlocality with critical phenomena.

Contribution

It introduces a novel approach using Bell function values to detect and analytically determine the critical point of topological phase transitions.

Findings

First derivative of BFV shows singular behavior at critical point

Critical point can be analytically calculated using BFV

BFV serves as a measure of quantum nonlocality beyond classical bounds

Abstract

We investigate the relation between Bell function values (BFV) of the reduced density matrix and the topological quantum phase transitions in the Kitaev-Castelnovo-Chamon model. % [Phys. Rev. B \textbf{77}, %054433 (2008)]. We find that the first order derivative of BFV exhibits singular behavior at the critical point and we propose that it can serve as a good and convenient marker for the transition point. More interestingly, the value of the critical point can be analytically obtained in this approach. Since the BFV serves as a measure of nonlocality when it is greater than the classical bound of the correlation functions, our work has established a link between quantum nonlocality and phase transitions.