Idioma:

On Weak Hopf Symmetry and Weak Hopf Quantum Double Model

Jia, Zhian ; Tan, Sheng ; Kaszlikowski, Dagomir ; Chang, Liang

Communications in mathematical physics, 2023-09, Vol.402 (3), p.3045-3107 [Periódico revisado por pares]

Berlin/Heidelberg: Springer Berlin Heidelberg

Texto completo disponível

Citações Citado por

Enviar para

Título:
On Weak Hopf Symmetry and Weak Hopf Quantum Double Model
Autor: Jia, Zhian ; Tan, Sheng ; Kaszlikowski, Dagomir ; Chang, Liang
Assuntos: Algebra ; Broken symmetry ; Classical and Quantum Gravitation ; Complex Systems ; Domain walls ; Equivalence ; Fields (mathematics) ; Group theory ; Lattices (mathematics) ; Lie groups ; Mathematical and Computational Physics ; Mathematical Physics ; Operators (mathematics) ; Physics ; Physics and Astronomy ; Quantum field theory ; Quantum Physics ; Quantum theory ; Relativity Theory ; Symmetry ; Tensors ; Theoretical ; Topology
É parte de: Communications in mathematical physics, 2023-09, Vol.402 (3), p.3045-3107
Descrição: Symmetry is a central concept for classical and quantum field theory, usually, symmetry is described by a finite group or Lie group. In this work, we introduce the weak Hopf algebra extension of symmetry, which arises naturally in anyonic quantum systems; and we establish the weak Hopf symmetry breaking theory based on the fusion closed set of anyons. As a concrete example, we implement a thorough investigation of the quantum double model based on a given weak Hopf algebra and show that the vacuum sector of the model has weak Hopf symmetry. The topological excitations and ribbon operators are discussed in detail. The gapped boundary and domain wall theories are also established. We show that the gapped boundary is algebraically determined by a comodule algebra, or equivalently, a module algebra; and the gapped domain wall is determined by the bicomodule algebra, or equivalently, a bimodule algebra. The microscopic lattice constructions of the gapped boundary and domain wall are discussed in detail. We also introduce the weak Hopf tensor network states, via which we solve the weak Hopf quantum double lattice models on closed and open surfaces. The duality of the quantum double phases is discussed in the last part.
Editor: Berlin/Heidelberg: Springer Berlin Heidelberg
Idioma: Inglês

Voltar para lista de resultados

Realização: Logos de Redes Sociais:

On Weak Hopf Symmetry and Weak Hopf Quantum Double Model

Jia, Zhian ; Tan, Sheng ; Kaszlikowski, Dagomir ; Chang, Liang

Berlin/Heidelberg: Springer Berlin Heidelberg

Buscando em bases de dados remotas. Favor aguardar.