Collective states of interacting $D(D_3)$ non-Abelian anyons

Abstract

We study the finite size spectrum of integrable quantum chains of interacting non-Abelian anyons constructed using the Drinfeld double of the dihedral group $D_3$. The gapless low energy modes are identified as the direct product of two conformal field theories which can be decomposed according to the residual symmetries of the chains subject to periodic boundary conditions.

11 pages

References in corpus (13)

• Non-Abelian Anyons and Topological Quantum Computation
• Kitaev-Heisenberg Model on Honeycomb Lattice: Possible Exotic Phases in Iridium Oxides $A_2$IrO${}_3$
• Interacting anyons in topological quantum liquids: The golden chain
• Collective States of Interacting Anyons, Edge States, and the Nucleation of Topological Liquids
• Condensation of achiral simple currents in topological lattice models: a Hamiltonian study of topological symmetry breaking
• Collective states of interacting Fibonacci anyons
• Simulations of quantum double models
• Topology driven quantum phase transitions in time-reversal invariant anyonic quantum liquids
• Simulation of anyons with tensor network algorithms
• Anyonic entanglement renormalization
• Ground-state phase diagram for a system of interacting, $D(D_3)$ non-Abelian anyons
• Solutions of the Yang-Baxter equation: descendants of the six-vertex model from the Drinfeld doubles of dihedral group algebras
• Integrable Hamiltonians with $D(D_n)$ symmetry from the Fateev-Zamolodchikov model

Cited by in corpus (1)

• The $D(D_3)$-anyon chain: integrable boundary conditions and excitation spectra