Dissipation-driven topological phase transitions in open quantum systems independent of system Hamiltonian

TL;DR

This paper demonstrates that in open quantum systems, dissipation operators solely determine topological phases and transitions, independent of the system Hamiltonian, with analytical and numerical evidence showing predictable topological changes driven by dissipation parameters.

Contribution

The study introduces a framework showing dissipation operators alone dictate topological invariants and transitions in open quantum systems, independent of the Hamiltonian.

Findings

Topological invariants depend only on dissipation operators.

Topological phase transitions occur at predictable critical times.

Bulk-edge correspondence is confirmed via entanglement spectrum analysis.

Abstract

We investigate dissipation-driven topological phase transitions in one-dimensional quantum open systems governed by the Lindblad equation with linear dissipation operators, which ensure the density matrix retains its Gaussian form throughout the dynamics. By employing the modular Hamiltonian framework, we rigorously demonstrate that the $\rm{Z}_2$ topological invariant characterizing steady states in one-dimensional class D systems is exclusively dependent on the dissipation operators, rather than the system Hamiltonian. Through a sudden quench protocol where the system evolves from the steady state of one Lindbladian to another, we reveal that topological transitions can occur at analytically predictable critical times, even when the initial and final steady states share identical topological indices. These transitions are shown, both analytically and numerically, to depend solely on dissipation parameters. Entanglement spectrum analysis demonstrates bulk-edge correspondence in non-equilibrium density matrices via coexisting single-particle gap closures (periodic boundaries) and topologically protected zero modes (open boundaries), directly underpinning the detection of dissipation-induced topology in quantum simulators.