Fate of fractional quantum Hall states in open quantum systems: characterization of correlated topological states for the full Liouvillian

Understand

Despite previous extensive analysis of open quantum systems described by the Lindblad equation, it is unclear whether correlated topological states, such as fractional quantum Hall states, are maintained even in the presence of the jump term.

• In this paper, we introduce the pseudo-spin Chern number of the Liouvillian which is computed by twisting the boundary conditions only for one of the subspaces of the doubled Hilbert space.
• The existence of such a topological invariant elucidates that the topological properties remain unchanged even in the presence of the jump term which does not close the gap of the effective non-Hermitian Hamiltonian (obtained by neglecting the jump term).
• In other words, the topological properties are encoded into an effective non-Hermitian Hamiltonian rather than the full Liouvillian.