Geometric phase and quantum phase transition in an inhomogeneous periodic XY spin-1/2 model

TL;DR

This paper investigates the geometric phase in an inhomogeneous XY spin-1/2 model, revealing multiple quantum phase transitions linked to Berry curvature behavior, using exact solutions via Jordan-Wigner transformation.

Contribution

It provides an exact analysis of geometric phases in a complex inhomogeneous XY model, uncovering multiple quantum critical points and their relation to Berry curvature.

Findings

Multiple quantum phase transition points identified.

Divergence or extremum of Berry curvature at transition points.

Model includes and extends familiar spin models.

Abstract

The notion of geometric phase has been recently introduced to analyze the quantum phase transitions of many-body systems from the geometrical perspective. In this work, we study the geometric phase of the ground state for an inhomogeneous period-two anisotropic XY model in a transverse field. This model encompasses a group of familiar spin models as its special cases and shows a richer critical behavior. The exact solution is obtained by mapping on a fermionic system through the Jordan-Wigner transformation and constructing the relevant canonical transformation to realize the diagonalization of the Hamiltonian coupled in the $k$-space. The results show that there may exist more than one quantum phase transition point at some parameter regions and these transition points correspond to the divergence or extremum properties of the Berry curvature.