Partition function of the Kitaev quantum double model

Abstract

We compute the degeneracy of energy levels in the Kitaev quantum double model for any discrete group $G$ on any planar graph forming the skeleton of a closed orientable surface of arbitrary genus. The derivation is based on the fusion rules of the properly identified vertex and plaquette excitations, which are selected among the anyons, i.e., the simple objects of the Drinfeld center $\mathcal{Z}({\mathrm{Vec}}_G)$. These degeneracies are given in terms of the corresponding $S$-matrix elements and allow one to obtain the exact finite-temperature partition function of the model, valid for any finite-size system.

39 pages, 15 figures, published version

References in corpus (27)

• Non-Abelian Anyons and Topological Quantum Computation
• Anyons in an exactly solved model and beyond
• String-net condensation: A physical mechanism for topological phases
• Probing Topological Spin Liquids on a Programmable Quantum Simulator
• Topological quantum order: stability under local perturbations
• Realization of an Error-Correcting Surface Code with Superconducting Qubits
• The Quantum Double Model with Boundary: Condensations and Symmetries
• Quantum memories at finite temperature
• Twisted Quantum Double Model of Topological Phases in Two--Dimension
• Autocorrelations and Thermal Fragility of Anyonic Loops in Topologically Quantum Ordered Systems
• Non-Abelian Topological Order and Anyons on a Trapped-Ion Processor
• Entanglement and topological entropy of the toric code at finite temperature
• Topological Order at Non-zero Temperature
• On thermalization in Kitaev's 2D model
• Mapping Kitaev's quantum double lattice models to Levin and Wen's string-net models
• Digital simulation of non-Abelian anyons with 68 programmable superconducting qubits
• Full Dyon Excitation Spectrum in Generalized Levin-Wen Models
• Discrete non-Abelian gauge theories in two-dimensional lattices and their realizations in Josephson-junction arrays
• Diagnosing Deconfinement and Topological Order
• Local topological order inhibits thermal stability in 2D
• Scaling law for topologically ordered systems at finite temperature
• Lattice Model for Fermionic Toric Code
• Universality Classes of Stabilizer Code Hamiltonians
• Anyons are not energy eigenspaces of quantum double Hamiltonians
• Topological and nontopological degeneracies in generalized string-net models
• Finite-temperature properties of string-net models
• Extended string-net models with all anyons at finite temperature