Extended string-net models with all anyons at finite temperature
arXiv:2502.01454 · doi:10.1103/PhysRevB.111.235405
Abstract
The string-net model describes a vast family of topological orders in two spatial dimensions. Here, we consider the effect of thermal fluctuations on these topological phases. In the original string-net model, the description of charge (vertex) excitations can be problematic. Therefore, in order to describe all anyon excitations, we study an extended model [Y. Hu et al., Phys. Rev. B 97, 195154 (2018)]. Building on recent methods, we compute the spectral degeneracies of excited states and obtain the exact partition function. In the thermodynamic limit, the latter is dominated by the trivial (vacuum) anyon, so that topological order is destroyed at any nonzero temperature. In contrast, in a finite-size system, order survives up to a finite temperature, revealing a nontrivial scaling between temperature and size similar to that of the one-dimensional classical Ising model. We confirm this scaling by computing the thermal average of several observables such as Wegner-Wilson loops and topological mutual information.
19 pages, 7 figures, 1 Table
References in corpus (33)
- Fault-tolerant quantum computation by anyons
- Non-Abelian Anyons and Topological Quantum Computation
- Anyons in an exactly solved model and beyond
- Topological entanglement entropy
- Detecting topological order in a ground state wave function
- String-net condensation: A physical mechanism for topological phases
- Zoo of quantum-topological phases of matter
- Area laws in quantum systems: mutual information and correlations
- Models for gapped boundaries and domain walls
- Exponential suppression of bit or phase flip errors with repetitive error correction
- Braid Topologies for Quantum Computation
- Autocorrelations and Thermal Fragility of Anyonic Loops in Topologically Quantum Ordered Systems
- Entanglement and topological entropy of the toric code at finite temperature
- Topological Order at Non-zero Temperature
- Anyons and matrix product operator algebras
- Gapped Domain Walls, Gapped Boundaries and Topological Degeneracy
- Topological quasiparticles and the holographic bulk-edge relation in 2+1D string-net models
- Generalizations and limitations of string-net models
- Full Dyon Excitation Spectrum in Generalized Levin-Wen Models
- Generalized string-net models: A thorough exposition
- Tube algebras, excitations statistics and compactification in gauge models of topological phases
- Generalized string-nets for unitary fusion categories without tetrahedral symmetry
- Topological order and topological entropy in classical systems
- Scaling law for topologically ordered systems at finite temperature
- Non-Abelian braiding of Fibonacci anyons with a superconducting processor
- Mapping between Morita equivalent string-net states with a constant depth quantum circuit
- Tensor-network approach to phase transitions in string-net models
- Anyons are not energy eigenspaces of quantum double Hamiltonians
- Signatures of broken parity and time-reversal symmetry in generalized string-net models
- Characteristic Properties of a Composite System of Topological Phases Separated by Gapped Domain Walls via an Exactly Solvable Hamiltonian Model
- Wegner-Wilson loops in string nets
- Topological and nontopological degeneracies in generalized string-net models
- Finite-temperature properties of string-net models