Two-Dimensional Density-Matrix Topological Fermionic Phases: Topological Uhlmann Numbers

Abstract

We construct a topological invariant that classifies density matrices of symmetry-protected topological orders in two-dimensional fermionic systems. As it is constructed out of the previously introduced Uhlmann phase, we refer to it as the topological Uhlmann number ${\mathrm{n}}_{\mathrm{U}}$. With it, we study thermal topological phases in several two-dimensional models of topological insulators and superconductors, computing phase diagrams where the temperature $T$ is on an equal footing with the coupling constants in the Hamiltonian. Moreover, we find novel thermal-topological transitions between two non-trivial phases in a model with high Chern numbers. At small temperature we recover the standard topological phases as the Uhlmann number approaches to the Chern number.

RevTex4 file, color figures. Close to published version

References in corpus (10)

• Non-Abelian Anyons and Topological Quantum Computation
• Classification of topological insulators and superconductors in three spatial dimensions
• Topological Field Theory of Time-Reversal Invariant Insulators
• Physics of three dimensional bosonic topological insulators: Surface Deconfined Criticality and Quantized Magnetoelectric Effect
• Topological flat band models with arbitrary Chern numbers
• On thermalization in Kitaev's 2D model
• Interferometric approach to measuring band topology in 2D optical lattices
• Topological indices for open and thermal systems via Uhlmann's phase
• Thermal Instability of Protected End States in a 1-D Topological Insulator
• Operational approach to the Uhlmann holonomy

Cited by in corpus (11)

• Topology of density matrices
• Mixed state dynamical quantum phase transition and emergent topology
• Topological indices for open and thermal systems via Uhlmann's phase
• Temperature effects in the band structure of topological insulators
• Universalities of thermodynamic signatures in topological phases
• Symmetry-protected Topological Phases at Finite Temperature
• Topological order of mixed states in quantum many-body systems
• Cellular dynamical mean-field theory study of an interacting topological honeycomb lattice model at finite temperature
• Decoherence Patterns of Topological Qubits from Majorana Modes
• Topology of a dissipative spin: dynamical Chern number, bath induced non-adiabaticity and a quantum dynamo effect
• Simulating dynamical quantum Hall effect with superconducting qubits