Uhlmann number in translational invariant systems

Abstract

We define the Uhlmann number as an extension of the Chern number, and we use this quantity to describe the topology of 2D translational invariant Fermionic systems at finite temperature. We consider two paradigmatic systems and we study the changes in their topology through the Uhlmann number. Through the linear response theory we linked two geometrical quantities of the system, the mean Uhlmann curvature and the Uhlmann number, to directly measurable physical quantities, i.e. the dynamical susceptibility and to the dynamical conductivity, respectively.

arXiv comment5 pages, 3 figures

References in corpus (27)

• Non-Abelian Anyons and Topological Quantum Computation
• 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
• Non-abelian statistics of half-quantum vortices in p-wave superconductors
• Topological Thouless Pumping of Ultracold Fermions
• Compatibility in Multiparameter Quantum Metrology
• Topology by dissipation
• Uhlmann Phase as a Topological Measure for One-Dimensional Fermion Systems
• Geometrical engineering of a two-bands Chern insulator in two dimensions with arbitrary topological index
• Multiparameter Gaussian Quantum Metrology
• Topology of density matrices
• Two-Dimensional Density-Matrix Topological Fermionic Phases: Topological Uhlmann Numbers
• Probing the topology of density matrices
• Topological indices for open and thermal systems via Uhlmann's phase
• Estimation of Gaussian quantum states
• Correlation effects on a topological insulator at finite temperatures
• Quantum response of dephasing open systems
• Symmetric Logarithmic Derivative of Fermionic Gaussian States
• 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
• Connections and Metrics Respecting Standard Purification
• 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
• Restoration of topological properties at finite temperatures in a heavy-fermion system

Cited by in corpus (15)

• Geometry of quantum phase transitions
• On quantumness in multi-parameter quantum estimation
• Topological Uhlmann phase transitions for a spin-j particle in a magnetic field
• Dynamic process and Uhlmann process: Incompatibility and dynamic phase of mixed quantum states
• Complexity in the Lipkin-Meshkov-Glick Model
• Universal shot-noise limit for quantum metrology with local Hamiltonians
• Haldane Model at finite temperature
• Topological order, mixed states and open systems
• Interferometric geometry from symmetry-broken Uhlmann gauge group with applications to topological phase transitions
• Uhlmann quench and geometric dynamic quantum phase transition of mixed states
• On critical properties of Berry curvature in Kitaev honeycomb model
• Gravitational Response of Topological Quantum States of Matter
• Quantum geometry and $X$-wave magnets with $X=p,d,f,g,i$
• Twin Hamiltonians, three types of the Dyson maps, and the probabilistic interpretation problem in quasi-Hermitian quantum mechanics
• Exploring Many-Body Quantum Geometry Beyond the Quantum Metric with Correlation Functions: A Time-Dependent Perspective