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

Uhlmann holonomy against Lindblad dynamics of topological systems at finite temperatures