Topological order and topological entropy in classical systems

Abstract

We show that the concept of topological order, introduced to describe ordered quantum systems which cannot be classified by broken symmetries, also applies to classical systems. Starting from a specific example, we show how to use pure state density matrices to construct corresponding thermally mixed ones that retain precisely half the original topological entropy, a result that we generalize to a whole class of quantum systems. Finally, we suggest that topological order and topological entropy may be useful in characterizing classical glassy systems.

(5 pages, 1 figure) v2: minor changes

References in corpus (5)

• Entanglement entropy of 2D conformal quantum critical points: hearing the shape of a quantum drum
• Bipartite entanglement and entropic boundary law in lattice spin systems
• Topological Entanglement Entropy in the Quantum Dimer Model on the Triangular Lattice
• A statistical mechanics view on Kitaev's proposal for quantum memories
• Quantum entanglement in states generated by bilocal group algebras

Cited by in corpus (47)

• Machine learning phases of matter
• Quantum entanglement in condensed matter systems
• Shannon and entanglement entropies of one- and two-dimensional critical wave functions
• Entanglement and topological entropy of the toric code at finite temperature
• Topological order in a 3D toric code at finite temperature
• Universal behavior beyond multifractality in quantum many-body systems
• Negativity and topological order in the toric code
• A quantum topological phase transition at the microscopic level
• Topological Entanglement Entropy of Z2 Spin liquids and Lattice Laughlin states
• Detecting Topological Order at Finite Temperature Using Entanglement Negativity
• Quantum mechanical and information theoretic view on classical glass transitions
• Participation spectroscopy and entanglement Hamiltonian of quantum spin models
• Intrinsic Mixed-state Topological Order
• A Noisy Approach to Intrinsically Mixed-State Topological Order
• Scaling law for topologically ordered systems at finite temperature
• Towards a classification of mixed-state topological orders in two dimensions
• Entanglement negativity and sudden death in the toric code at finite temperature
• Topological quantum phase transition in bond-alternating spin-1/2 Heisenberg chains
• Topological Sector Fluctuations and Curie Law Crossover in Spin Ice
• On the stability of topological phases on a lattice
• When opposites repel: from metastability to extended chiral spin textures in spin ice with short-range topological-defect interactions
• Ice Rule Fragility via Topological Charge Transfer in Artificial Colloidal Ice
• Classical Topological Order in Kagome Ice
• Entanglement Entropy and Mutual Information in Bose-Einstein Condensates
• Exact results on the quench dynamics of the entanglement entropy in the toric code
• Kagome qubit ice
• Dynamic scaling of topological ordering in classical systems
• The Kitaev-Ising model, Transition between topological and ferromagnetic order
• Topological order, entanglement, and quantum memory at finite temperature
• A complete characterization of the spectrum of the Kitaev model on spin ladders
• Renyi entropies for classical stringnet models
• Block Entanglement Entropy of Ground States with Long-Range Magnetic Order
• Distilling topological entropy from single entanglement measures on projected systems
• Thermalization of Topological Entropy after a Quantum Quench
• Quench dynamics of topological quantum phase transition in Wen-plaquette model
• A superconducting circuit realization of combinatorial gauge symmetry
• A Rényi entropy perspective on topological order in classical toric code models
• Classical Topological Order in Abelian and Non-Abelian Generalized Height Models
• Steady-state topological order
• Anderson localization of emergent quasiparticles: Spinon and vison interplay at finite temperature in a ${\mathbb{Z}}_2$ gauge theory in three dimensions
• Geometric clusters in the overlap of the Ising model
• Entanglement in topological systems
• Universal Renyi mutual information in classical systems: the case of kagome ice
• Topology by Design in Magnetic nano-Materials: Artificial Spin Ice
• Extended string-net models with all anyons at finite temperature
• Attention to Quantum Complexity
• Topology-driven phase transitions in the classical monomer-dimer-loop model