Topology of density matrices

2015/01/31 by Jan Carl Budich, Sebastian Diehl · 125 citations
Mathematics · Physics and Astronomy · #Combinatorics #Density matrix #Gauge (firearms) #Gauge theory #Hilbert space #Limit (mathematics) #Mathematical analysis #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Quantum #Quantum many-body systems #Quantum mechanics #Space (punctuation) #Theoretical physics #Topological Materials and Phenomena #Topological insulator #Topology (electrical circuits) #cond-mat.mes-hall #quant-ph

paper · pdf · doi:10.1103/physrevb.91.165140

published in Physical Review B 91(16) (American Physical Society)

arxiv created 2015/04/30 · openalex publication_date 2015/04/30 · arxiv updated 2015/05/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Can topologically non-trivial states, such as those in topological insulators and superconductors, arise in the mixed states of open quantum systems? By imposing special constraints on the gauge structure of the density matrices which describe open quantum systems, the authors find non-trivial topological invariants showing that topological phenomena can be generalized to mixed states. The method is illustrated with an analysis of Chern insulators at finite temperature.

Citations

• Classification of topological insulators and superconductors in three spatial dimensions
• Appearance of Gauge Structure in Simple Dynamical Systems
• Two-Dimensional Density-Matrix Topological Fermionic Phases: Topological Uhlmann Numbers
• Topological insulators and superconductors
• Dissipative preparation of Chern insulators
• Quantized Hall Conductance in a Two-Dimensional Periodic Potential
• Holonomy, the Quantum Adiabatic Theorem, and Berry's Phase
• Quantal phase factors accompanying adiabatic changes
• Topological Insulators
• Characteristic Classes of Hermitian Manifolds

Cited by

• Topological characterization of one-dimensional open fermionic systems
• Temperature dependence of the topological phase transition of BiTeI from first principles