Aharonov-Anandan phase in Lipkin-Meskov-Glick model

TL;DR

This paper investigates the non-adiabatic Aharonov-Anandan geometric phase in the Lipkin-Meshkov-Glick model, extending the understanding of geometric phases beyond the adiabatic regime with generalized formulas.

Contribution

It introduces a method to calculate both non-degenerate and degenerate geometric phases in the Lipkin-Meshkov-Glick model, generalizing Floquet theory for this purpose.

Findings

Derived a general formula for degenerate geometric phases.

Analyzed non-adiabatic geometric phases in the Lipkin-Meshkov-Glick model.

Extended Floquet theorem for operator decomposition.

Abstract

In the system of several interacting spins, geometric phases have been researched intensively.However, the studies are mainly focused on the adiabatic case (Berry phase), so it is necessary for us to study the non-adiabatic counterpart (Aharonov and Anandan phase). In this paper, we analyze both the non-degenerate and degenerate geometric phase of Lipkin-Meskov-Glick type model, which has many application in Bose-Einstein condensates and entanglement theory. Furthermore, in order to calculate degenerate geometric phases, the Floquet theorem and decomposition of operator are generalized. And the general formula is achieved.