Topological order of mixed states in quantum many-body systems

TL;DR

This paper extends the concept of topological order to mixed states in quantum many-body systems, analyzing its robustness and classification at finite temperatures, with implications for understanding topological phases like the quantum Hall effect.

Contribution

It generalizes topological order definitions to mixed states in correlated many-body systems and examines their robustness under various perturbations.

Findings

Topological order can be extended to density matrices of many-body systems.

Robustness of topological order depends on the nature of perturbations and system openness.

Classifies finite-temperature topological phases, including the classical Hall effect.

Abstract

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. While it is intrinsically protected against local perturbations of arbitrary strength in an infinite closed quantum system, purely local perturbations can destroy topological order in open systems coupled to baths if the coupling is sufficiently strong. We discuss our classification scheme using the finite-temperature quantum Hall states and point out that the classical Hall effect can be understood as a finite temperature topological phase.