Uhlmann holonomy against Lindblad dynamics of topological systems at finite temperatures

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.

arXiv comment10 pages, 4 figures, submitted

References in corpus (32)

• Topological Insulators
• Topological insulators and superconductors
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Unpaired Majorana fermions in quantum wires
• Topological Insulators in Three Dimensions
• Symmetry and Topology in Non-Hermitian Physics
• Direct Measurement of the Zak phase in Topological Bloch Bands
• Holonomic Quantum Computation
• An equivalent expression of Z2 Topological Invariant for band insulators using Non-Abelian Berry's connection
• Topological quantization of the spin Hall effect in two-dimensional paramagnetic semiconductors
• Non-Hermitian skin effect and chiral damping in open quantum systems
• Geometric phases for mixed states in interferometry
• Experimental Realization of Nonadiabatic Holonomic Quantum Computation
• Non-Adiabatic Holonomic Quantum Computation in Decoherence-Free Subspaces
• Topology by dissipation
• Uhlmann Phase as a Topological Measure for One-Dimensional Fermion Systems
• Holonomic Quantum Control by Coherent Optical Excitation in Diamond
• A quantum algorithm for evolving open quantum dynamics on quantum computing devices
• Digital quantum simulation of open quantum systems using quantum imaginary time evolution
• Topology of density matrices
• Two-Dimensional Density-Matrix Topological Fermionic Phases: Topological Uhlmann Numbers
• Probing the topology of density matrices
• Topological indices for open and thermal systems via Uhlmann's phase
• Observation of topological Uhlmann phases with superconducting qubits
• Fault-tolerant holonomic quantum computation
• Holonomic quantum computation in the presence of decoherence
• Symmetry-protected Topological Phases at Finite Temperature
• Uhlmann's geometric phase in presence of isotropic decoherence
• Finite-temperature topological phase transitions of spin-$j$ systems in Uhlmann processes: General formalism and experimental protocols
• Topological Uhlmann phase transitions for a spin-j particle in a magnetic field
• Dynamic process and Uhlmann process: Incompatibility and dynamic phase of mixed quantum states
• Thermal Uhlmann Chern number from the Uhlmann connection for extracting topological properties of mixed states

Cited by in corpus (4)

• Phonon-induced breakdown of Thouless pumping in the Rice-Mele-Holstein model
• Role of Bath-Induced Many-Body Interactions in the Dissipative Phases of the Su-Schrieffer-Heeger Model
• Thermal Uhlmann phase in a locally driven two-spin system
• The Uhlmann Phase Winding in Bose-Einstein Condensates at Finite Temperature