Galois conjugates of String-net Model
arXiv:2108.05730 · doi:10.1103/PhysRevD.105.065009
Abstract
We revisit a class of non-Hermitian topological models that are Galois conjugates of their Hermitian counter parts. Particularly, these are Galois conjugates of unitary string-net models. We demonstrate these models necessarily have real spectra, and that topological numbers are recovered as matrix elements of operators evaluated in appropriate bi-orthogonal basis, that we conveniently reformulate as a concomitant Hilbert space here. We also compute in the bi-orthogonal basis thetopological entanglement entropy, demonstrating that its real part is related to the quantum dimension of the topological order. While we focus mostly on the Yang-Lee model, the results in the paper apply generally to Galois conjugates.
arXiv comment10 pages, 2 figures, Chen and Lao are co-first authors of the manuscript
References in corpus (29)
- Making Sense of Non-Hermitian Hamiltonians
- Detecting topological order in a ground state wave function
- String-net condensation: A physical mechanism for topological phases
- PT-Symmetric Quantum Mechanics
- Pseudo-Hermitian Representation of Quantum Mechanics
- Twisted Quantum Double Model of Topological Phases in Two--Dimension
- Lecture Notes of Tensor Network Contractions
- Entanglement spectrum and entropy in topological non-Hermitian systems and non-unitary conformal field theories
- Anyons and matrix product operator algebras
- Explicit tensor network representation for the ground states of string-net models
- Generalizations and limitations of string-net models
- Topological Field Theory of Non-Hermitian Systems
- Mapping topological to conformal field theories through strange correlators
- Biorthogonal Quantum Systems
- Generalized string-nets for unitary fusion categories without tetrahedral symmetry
- Microscopic models of interacting Yang-Lee anyons
- Characterizing Topological Order with Matrix Product Operators
- Experimental Identification of Non-Abelian Topological Orders on a Quantum Simulator
- Non-Hermitian Dynamic Strings and Anomalous Topological Degeneracy on non-Hermitian Toric-code Model with Parity-time Symmetry
- Galois Conjugates of Topological Phases
- Planar Super-Landau Models Revisited
- Galois conjugated tensor fusion categories and non-unitary CFT
- Density Matrix Formalism for PT-Symmetric Non-Hermitian Hamiltonians with the Lindblad Equation
- Entanglement, non-Hermiticity, and duality
- PT-symmetry and its spontaneous breakdown explained by anti-linearity
- Characterization of topological phase transitions from a non-Abelian topological state and its Galois conjugate through condensation and confinement order parameters
- Non-Hermitian effects of the intrinsic signs in topologically ordered wavefunctions
- Quasi-hermitian Quantum Mechanics in Phase Space
- Tensor-product representations for string-net condensed states