Symmetry-Preserving Quadratic Lindbladian and Dissipation Driven Topological Transitions in Gaussian States

Abstract

The dynamical evolution of an open quantum system can be governed by the Lindblad equation of the density matrix. In this paper, we propose to characterize the density matrix topology by the topological invariant of its modular Hamiltonian. Since the topological classification of such Hamiltonians depends on their symmetry classes, a primary issue we address is determining the requirement for the Lindbladian operators, under which the modular Hamiltonian can preserve its symmetry class during the dynamical evolution. We solve this problem for the fermionic Gaussian state and for the modular Hamiltonian being a quadratic operator of a set of fermionic operators. When these conditions are satisfied, along with a nontrivial topological classification of the symmetry class of the modular Hamiltonian, a topological transition can occur as time evolves. We present two examples of dissipation-driven topological transitions where the modular Hamiltonian lies in the AIII class with U(1) symmetry and the DIII class without U(1) symmetry. By a finite size scaling, we show that this density matrix topology transition occurs at a finite time. We also present the physical signature of this transition.

8 pages, 2 figure

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Cited by in corpus (12)

• Many-Body Open Quantum Systems
• Reviving the Lieb-Schultz-Mattis Theorem in Open Quantum Systems
• Interaction-induced topological phase transition at finite temperature
• Spontaneous symmetry breaking in open quantum systems: strong, weak, and strong-to-weak
• Topologically Ordered Steady States in Open Quantum Systems
• Mixed-state phase transitions in spin-Holstein models
• Probing the Topology of Fermionic Gaussian Mixed States with {U(1)} symmetry by Full Counting Statistics
• Finite-temperature topological invariant for higher-order topological insulators
• Dynamic transition of the density-matrix topology under parity-time symmetry
• Dissipation-driven topological phase transitions in open quantum systems independent of system Hamiltonian
• Symmetry classification correspondence between quadratic Lindbladians and their steady states
• Phase Transition of Topological Index driven by Dephasing