Geometric phases and quantum phase transitions

TL;DR

This paper reviews the recent discovery of a fundamental link between geometric phases and quantum phase transitions, highlighting how geometric phases exhibit universal behavior near critical points in many-body systems.

Contribution

It summarizes recent advances establishing a connection between geometric phases and quantum criticality, revealing universal and scaling behaviors in many-body ground states.

Findings

Geometric phase exhibits universality near critical points.

Connection between geometric quantities and quantum phase transitions.

Potential for interdisciplinary research and new insights.

Abstract

Quantum phase transition is one of the main interests in the field of condensed matter physics, while geometric phase is a fundamental concept and has attracted considerable interest in the field of quantum mechanics. However, no relevant relation was recognized before recent work. In this paper, we present a review of the connection recently established between these two interesting fields: investigations in the geometric phase of the many-body systems have revealed so-called "criticality of geometric phase", in which geometric phase associated with the many-body ground state exhibits universality, or scaling behavior in the vicinity of the critical point. In addition, we address the recent advances on the connection of some other geometric quantities and quantum phase transitions. The closed relation recently recognized between quantum phase transitions and some of geometric quantities may open attractive avenues and fruitful dialog between different scientific communities.