Symmetry-preserving quadratic Lindbladian and dissipation driven topological transitions in Gaussian states
Year: 2024
Type: article
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.
Source: Reports on Progress in Physics
Authors: Liang Mao, Fan Yang, Hui Zhai
Institution: Tsinghua University
Language: English
Subfield: Condensed Matter Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Funder: Tsinghua University
OpenAlex ID: W4399863501