Quantized Uhlmann phase and edge-state suppression of quantum transport in Lindblad dynamics

The Uhlmann phase is a generalization of the Berry phase from pure states to mixed states. Quantized Uhlmann phase has been found in many quantum systems at finite temperatures, revealing its potential to be a finite-temperature topological indicator. We show that the quantization of the Uhlmann phase may survive quantum jumps from system-reservoir couplings by using the Lindblad equation to simulate quantum dynamics of topological systems. The robustness of the Uhlmann phase offers hope for finite-temperature quantum computation utilizing the Uhlmann holonomy. By introducing a density or temperature difference through the reservoirs and monitoring the Lindblad quantum dynamics, we show that the Su-Schrieffer-Heeger model exhibits edge-state suppression of quantum transport. In contrast, the bandwidth of the Kitaev chain dominates its dynamics, leaving no observable topological signature in transport at the single-particle level.