Geometric Phases for Mixed States of the Kitaev Chain

TL;DR

This paper investigates different geometric phases in the Kitaev chain at finite temperature, highlighting their distinct physical implications and potential for understanding topological properties in mixed states.

Contribution

It provides a detailed analysis of Uhlmann's geometric phase and introduces a new phase relevant to interferometry, comparing their behaviors in the Kitaev chain.

Findings

Uhlmann's phase captures different physics than the Berry phase.

The interferometric phase closely mirrors the Berry phase behavior.

Uhlmann's phase may not serve as a topological order parameter.

Abstract

The Berry phase has found applications in building topological order parameters for certain condensed matter systems. The question whether some geometric phase for mixed states can serve the same purpose has been raised, and proposals are on the table. We analyze the intricate behaviour of Uhlmann's geometric phase in the Kitaev chain at finite temperature, and then argue that it captures quite different physics from that intended. We also analyze the behaviour of a geometric phase introduced in the context of interferometry. For the Kitaev chain, this phase closely mirrors that of the Berry phase, and we argue that it merits further investigation.