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The dynamical evolution of an open quantum system can be governed by theLindblad equation of the density matrix. In this letter, we propose that thedensity matrix topology can undergo a transition during the Lindbladiandynamical evolution. Here we characterize the density matrix topology by thetopological invariant of its modular Hamiltonian. We focus on the fermionicGaussian state, where the modular Hamiltonian is a quadratic operator of a setof fermionic operators. The topological classification of such Hamiltoniansdepends on their symmetry classes. Hence, a primary issue we deal with in thiswork is to determine the requirement for the Lindbladian operators, under whichthe modular Hamiltonian can maintain its symmetry class during the dynamicalevolution. When these conditions are satisfied, along with a nontrivialtopological classification of the symmetry class of the modular Hamiltonian, atopological transition can occur as time evolves. We present two examples ofdissipation driven topological transitions where the modular Hamiltonian liesin the AIII class with U(1) symmetry and in the DIII class without U(1)symmetry, respectively. As a manifestation of the topological transition, wepresent the signature of the eigenvalues of the density matrix at thetransition point.

Dissipation Dynamics Driven Transitions of the Density Matrix Topology