Quantum phase transition in the one-dimensional period-two and uniform compass model

TL;DR

This paper investigates quantum phase transitions in one-dimensional period-two and uniform quantum compass models using exact solutions, revealing critical behaviors in fidelity, entanglement, and correlation functions.

Contribution

It provides exact solutions and detailed analysis of quantum phase transitions in both period-two and uniform quantum compass models, highlighting differences in correlation behaviors.

Findings

Fidelity and susceptibility change significantly at the critical point

Pseudo-spin concurrence gap scales as 1/N

Correlation length diverges at the critical point

Abstract

Quantum phase transition in the one-dimensional period-two and uniform quantum compass model are studied by using the pseudo-spin transformation method and the trace map method. The exact solutions are presented, the fidelity, the nearest-neighbor pseudo-spin entanglement, spin and pseudo-spin correlation functions are then calculated. At the critical point, the fidelity and its susceptibility change substantially, the gap of pseudo-spin concurrence is observed, which scales as $1/N$ (N is system size). The spin correlation functions show smooth behavior around the critical point. In the period-two chain, the pseudo-spin correlation functions exhibit a oscillating behavior, which is absent in the unform chain. The divergent correlation length at the critical point is demonstrated in the general trend for both cases.