Pseudo-Hermitian Levin-Wen models from non-semisimple TQFTs
arXiv:2108.10798 · doi:10.1016/j.aop.2022.168937
Abstract
We construct large classes of exactly solvable pseudo-Hermitian 2D spin Hamiltonians. The ground states of these systems depend only on the spatial topology of the system. We identify the ground state system on a surface with the value assigned to the surface by a non-semisimple TQFT generalizing the Turaev-Viro model. A non-trivial example arises from a non-semisimple subcategory of representations of quantum sl(2) where the quantum parameter is specialized to a root of unity.
arXiv comment21 pages, tikz diagrams, 2 figures
References in corpus (25)
- Fault-tolerant quantum computation by anyons
- Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
- Pseudo-Hermiticity versus PT Symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian
- String-net condensation: A physical mechanism for topological phases
- Pseudo-Hermiticity versus PT-Symmetry II: A complete characterizatio n of non-Hermitian Hamiltonians with a real spectrum
- Pseudo-Hermiticity versus PT-Symmetry III: Equivalence of pseudo-Her miticity and the presence of antilinear symmetries
- Introduction to PT-Symmetric Quantum Theory
- Models for gapped boundaries and domain walls
- Invariants of 3-manifolds and projective representations of mapping class groups via quantum groups at roots of unity
- Quantum computation with Turaev-Viro codes
- Generalizations and limitations of string-net models
- Quantum invariants of 3-manifolds via link surgery presentations and non-semi-simple categories
- Generalized string-net models: A thorough exposition
- Ground State Degeneracy in the Levin-Wen Model for Topological Phases
- String-net model of Turaev-Viro invariants
- Topology driven quantum phase transitions in time-reversal invariant anyonic quantum liquids
- Pseudo-Unitary Operators and Pseudo-Unitary Quantum Dynamics
- Generalized string-nets for unitary fusion categories without tetrahedral symmetry
- Some remarks on the unrolled quantum group of sl(2)
- Is Pseudo-Hermitian Quantum Mechanics an Indefinite-Metric Quantum Theory?
- Non-Semisimple Quantum Invariants and TQFTs from Small and Unrolled Quantum Goups
- Kitaev's Lattice Model and Turaev-Viro TQFTs
- Topological invariants from non-restricted quantum groups
- Mapping Class Group Representations From Non-Semisimple TQFTs
- Polynomial 6j-Symbols and States Sums
Cited by in corpus (4)
- Universal quantum computation using Ising anyons from a non-semisimple Topological Quantum Field Theory
- A Hermitian TQFT from a non-semisimple category of quantum sl(2)-modules
- Non-semisimple Levin-Wen Models and Hermitian TQFTs from quantum (super)groups
- Density and unitarity of the Burau representation from a non-semisimple TQFT