Geometric Phase and Quantum Phase Transition : Two-Band Model

TL;DR

This paper presents an exact analytical method to connect geometric phase with quantum phase transitions in a two-band model, demonstrating how geometric phase behavior signals phase changes related to the energy gap.

Contribution

It introduces an exact calculation approach for geometric phase in the two-band model, advancing understanding of its relation to quantum phase transitions.

Findings

Geometric phase behavior varies with phase transition

Exact calculation method established

Geometric phase linked to energy gap dynamics

Abstract

The connection between the geometric phase and quantum phase transition has been discussed extensively in the two-band model. By introducing the twist operator, the geometric phase can be defined by calculating its ground-state expectation value. In contrast to the previous numerical examinations, our discussion presents an exact calculation for the determination of the geometric phase. Through two representative examples, our calculation shows the intimate connection between the geometric phase and phase transition: different behaviors of the geometric phase can be identified in this paper, which are directly related to the energy gap above the ground state.