Topological order of mixed states in quantum many-body systems

Understand

Topological order has become a new paradigm to distinguish ground states of interacting many-body systems without conventional long-range order.

• Here we discuss possible extensions of this concept to density matrices describing statistical ensembles.
• For a large class of quasi-thermal states, which can be realized as thermal states of some quasi-local Hamiltonian, we generalize earlier definitions of density matrix topology to generic many-body systems with strong correlations.
• We point out that the robustness of topological order, defined as a pattern of long-range entanglement, depends crucially on the perturbations under consideration.