Fidelity susceptibility and geometric phase in critical phenomenon

TL;DR

This paper explores the relationship between fidelity susceptibility, geometric phase, and quantum phase transitions in various models, introducing new methods and verifying their effectiveness in signaling critical phenomena.

Contribution

It establishes a connection between Lie algebra structures and fidelity susceptibility, and applies a novel calculation method to complex quantum systems.

Findings

Fidelity susceptibility signals quantum phase transitions in SU(2) and SU(1,1) models.

Derived geometric phase in these models during fidelity calculations.

Applied new methods to 2D XXZ model and Bose-Einstein condensate.

Abstract

Motivated by recent development in quantum fidelity and fidelity susceptibility, we study relations among Lie algebra, fidelity susceptibility and quantum phase transition for a two-state system and the Lipkin-Meshkov-Glick model. We get the fidelity susceptibility for SU(2) and SU(1,1) algebraic structure models. From this relation, the validity of the fidelity susceptibility to signal for the quantum phase transition is also verified in these two systems. At the same time, we obtain the geometric phase in these two systems in the process of calculating the fidelity susceptibility. In addition, the new method of calculating fidelity susceptibility has been applied to explore the two-dimensional XXZ model and the Bose-Einstein condensate(BEC).