Mixed-state geometric phases of coherent and squeezed spin states

TL;DR

This paper investigates two types of mixed-state geometric phases in spin coherent and squeezed states, revealing temperature-dependent topological transitions and smooth variations, with potential implications for quantum spin system simulations.

Contribution

It provides exact solutions and numerical analysis of Uhlmann and interferometric geometric phases in spin states, highlighting temperature-induced topological phase transitions and their dependence on state parameters.

Findings

Uhlmann phase shows finite-temperature topological transitions in CSSs.

Interferometric geometric phase exhibits abrupt jumps with temperature.

Two-axis SSS shows no topological transitions, phases vary smoothly.

Abstract

Two mixed-state geometric phases, known as the Uhlmann phase and interferometric geometric phase (IGP), of spin coherent states (CSSs) and spin squeezed states (SSSs) are analyzed. Exact solutions and numerical results of selected examples are presented. For the $j = 3/2$ CSS, the Uhlmann phase exhibits finite-temperature topological phase transitions characterized by abrupt jumps. The IGP for the same state similarly shows discontinuous jumps as the temperature varies. In the case of the $j = 1$ one-axis SSS, both Uhlmann phase and IGP display discrete finite-temperature jumps. By contrast, the $j = 1$ two-axis SSS shows no such transitions because the Uhlmann phase and IGP both vary smoothly with temperature. We also briefly discuss potential realizations and simulations related to these phenomena in spin systems.