Geometric phases and criticality in spin chain systems

TL;DR

This paper demonstrates how geometric phases can be used to identify critical regions in spin chain systems, specifically the anisotropic XY model, without requiring a quantum phase transition, with potential realization in ultra-cold atoms.

Contribution

It establishes a novel link between geometric phases and criticality in spin chains, providing an analytical method to detect critical regions without phase transitions.

Findings

Geometric phases correlate with critical points in spin chains.

Analytical evaluation of geometric phases for the XY model.

Potential implementation in ultra-cold atomic systems.

Abstract

A relation between geometric phases and criticality of spin chains is established. As a result, we show how geometric phases can be exploited as a tool to detect regions of criticality without having to undergo a quantum phase transition. We analytically evaluate the geometric phase that correspond to the ground and excited states of the anisotropic XY model in the presence of a transverse magnetic field when the direction of the anisotropy is adiabatically rotated. Ultra-cold atoms in optical lattices are presented as a possible physical realization.