Uhlmann holonomy against Lindblad dynamics of topological systems at finite temperatures

TL;DR

This paper investigates the robustness of the Uhlmann holonomy as a topological invariant in quantum systems under Lindblad dynamics at finite temperatures, demonstrating its quantization under specific conditions.

Contribution

It provides a systematic analysis of the Uhlmann phase's behavior in topological systems influenced by Lindblad-type environmental interactions, highlighting conditions for topological protection.

Findings

Uhlmann phase remains quantized for topological initial states with certain Lindblad operators.

Topological protection persists at finite temperatures under specific system-environment couplings.

Quantization of the Uhlmann phase is not universal but depends on the nature of the Lindblad dynamics.

Abstract

The Uhlmann phase, which reflects the holonomy as the purified state of a density matrix traverses a loop in the parameter space, has been used to characterize topological properties of several systems at finite temperatures. We test the Uhlmann holonomy against various system-environment couplings in quantum dynamics described by the Lindblad equations of three topological systems, including the Su-Schrieffer-Heeger (SSH) model, Kitaev chain, and Bernevig-Hughes-Zhang (BHZ) model. The Uhlmann phase is shown to remain quantized in all the examples if the initial state is topological and only certain types of the Lindblad jump operators are present. Topological protection at finite temperatures against environmental effects in quantum dynamics is therefore demonstrated albeit only for a restricted class of system-environment couplings.