Anyon Condensation: Coherent states, Symmetry Enriched Topological Phases, Goldstone Theorem, and Dynamical Rearrangement of Symmetry

Abstract

Although the mathematics of anyon condensation in topological phases has been studied intensively in recent years, a proof of its physical existence is tantamount to constructing an effective Hamiltonian theory. In this paper, we concretely establish the physical foundation of anyon condensation by building the effective Hamiltonian and the Hilbert space, in which we explicitly construct the vacuum of the condensed phase as the coherent states that are the eigenstates of the creation operators that create the condensate anyons. Along with this construction, which is analogous to Laughlin's construction of wavefunctions of fractional quantum hall states, we generalize the Goldstone theorem in the usual spontaneous symmetry breaking paradigm to the case of anyon condensation. We then prove that the condensed phase is a symmetry enriched (protected) topological phase by directly constructing the corresponding symmetry transformations, which can be considered as a generalization of the Bogoliubov transformation.

References in corpus (7)

• Condensate induced transitions between topologically ordered phases
• A classification of symmetry enriched topological phases with exactly solvable models
• Genons, twist defects, and projective non-Abelian braiding statistics
• Twisted Quantum Double Model of Topological Phases in Two--Dimension
• Fractional topological insulators in three dimensions
• Ground State Degeneracy of Topological Phases on Open Surfaces
• Lagrangian subcategories and braided tensor equivalences of twisted quantum doubles of finite groups

Cited by in corpus (12)

• Topological Holography: Towards a Unification of Landau and Beyond-Landau Physics
• Gapped boundaries of (3+1)d topological orders
• Emergent XY* transition driven by symmetry fractionalization and anyon condensation
• Extend The Levin-Wen Model To Two-dimensional Topological Orders With Gapped Boundary Junctions
• Symmetry Fractionalized (Irrationalized) Fusion Rules and Two Domain-Wall Verlinde Formulae
• Characteristic Properties of a Composite System of Topological Phases Separated by Gapped Domain Walls via an Exactly Solvable Hamiltonian Model
• Nonabelian Anyon Condensation in 2+1d topological orders: A String-Net Model Realization
• Noninvertible Gauge Symmetry in (2+1)d Topological Orders: A String-Net Model Realization
• Competing automorphisms and disordered Floquet codes
• Classification of Gapped Domain Walls of Topological Orders in 2+1 dimensions: A Levin-Wen Model Realization
• Nonlinear Symmetry-Fragmentation of Nonabelian Anyons In Symmetry-Enriched Topological Phases: A String-Net Model Realization
• Fourier-transformed gauge theory models of three-dimensional topological orders with gapped boundaries