Scaling of geometric phases close to quantum phase transition in the XY chain

TL;DR

This paper demonstrates that the geometric phase in the XY model exhibits scaling behavior near quantum phase transitions, diverges at critical points, and reveals universal properties applicable to many-body systems.

Contribution

It establishes a general relation between geometric phases and quantum phase transitions, showing universality and critical scaling in the XY model and beyond.

Findings

Geometric phase diverges at critical magnetic field

Universal critical properties of geometric phase verified

Relation between geometric phase and quantum phase transitions is general

Abstract

We show that geometric phase of the ground state in the XY model obeys scaling behavior in the vicinity of a quantum phase transition. In particular we find that geometric phase is non-analytical and its derivative with respect to the field strength diverges at the critical magnetic field. Furthermore, universality in the critical properties of the geometric phase in a family of models is verified. In addition, since quantum phase transition occurs at a level crossing or avoided level crossing and these level structures can be captured by Berry curvature, the established relation between geometric phase and quantum phase transitions is not a specific property of the XY model, but a very general result of many-body systems.