Finite temperature geometric properties of the Kitaev honeycomb model

Abstract

We study finite temperature topological phase transitions of the Kitaev's spin honeycomb model in the vortex-free sector with the use of the recently introduced mean Uhlmann curvature. We employ an appropriate Fermionisation procedure to study the system as a two-band p-wave superconductor described by a BdG Hamiltonian. This allows to study relevant quantities such as Berry and mean Uhlmann curvatures in a simple setting. More specifically, we consider the spin honeycomb in the presence of an external magnetic field breaking time reversal symmetry. The introduction of such an external perturbation opens a gap in the phase of the system characterised by non-Abelian statistics, and makes the model to belong to a symmetry protected class, so that the Uhmann number can be analysed. We first consider the Berry curvature on a particular evolution line over the phase diagram. The mean Uhlmann curvature and the Uhlmann number are then analysed considering the system to be in a Gibbs state at finite temperature. Then, we show that the mean Uhlmann curvature describes a cross-over effect of the phases at high temperature. We also find an interesting nonmonotonic behaviour of the Uhlmann number as a function of the temperature in the trivial phase, which is due to the partial filling of the conduction band around Dirac points.

arXiv comment11 pages, 8 figures

References in corpus (37)

• Fault-tolerant quantum computation by anyons
• Non-Abelian Anyons and Topological Quantum Computation
• Anyons in an exactly solved model and beyond
• Classification of topological insulators and superconductors in three spatial dimensions
• Classification of topological quantum matter with symmetries
• Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Periodic table for topological insulators and superconductors
• Topological Thouless Pumping of Ultracold Fermions
• Fidelity approach to quantum phase transitions
• Quantum critical scaling of the geometric tensors
• The Flux-Phase of the Half-Filled Band
• Topology by dissipation
• Topological phases and surface flat bands in superconductors without inversion symmetry
• Geometric phases and criticality in spin chain systems
• Uhlmann Phase as a Topological Measure for One-Dimensional Fermion Systems
• Fidelity susceptibility and long-range correlation in the Kitaev honeycomb model
• Geometrical engineering of a two-bands Chern insulator in two dimensions with arbitrary topological index
• Topology of density matrices
• Two-Dimensional Density-Matrix Topological Fermionic Phases: Topological Uhlmann Numbers
• Probing the topology of density matrices
• Effects of Lévy noise on the dynamics of sine-Gordon solitons in long Josephson junctions
• Topological indices for open and thermal systems via Uhlmann's phase
• Observation of topological Uhlmann phases with superconducting qubits
• Topological phases and quantum computation
• A Description of Kitaev's Honeycomb Model with Toric-Code Stabilizers
• Symmetric Logarithmic Derivative of Fermionic Gaussian States
• Quantum response of dephasing open systems
• Spectrum of the non-abelian phase in Kitaev's honeycomb lattice model
• Topological degeneracy and vortex manipulation in Kitaev's honeycomb model
• Topological Blocking in Quantum Quench Dynamics
• Reservoir-induced Thouless pumping and symmetry protected topological order in open quantum chains
• The Uhlmann connection in fermionic systems undergoing phase transitions
• Topological order of mixed states in quantum many-body systems
• Kitaev spin models from topological nanowire networks
• Quantum dissipative dynamics of a bistable system in the sub-Ohmic to super-Ohmic regime
• Thermal Uhlmann Chern number from the Uhlmann connection for extracting topological properties of mixed states

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