Exact solution of the $D_3$ non-Abelian anyon chain

Abstract

Commuting transfer matrices for linear chains of interacting non-Abelian anyons from the two-dimensional irreducible representation of the dihedral group $D_3$ (or, equivalently, the integer sector of the $su(2{)}_4$ spin-$1$ chain) are constructed using the spin-anyon correspondence to a $D_3$-symmetric formulation of the XXZ Heisenberg spin chain. The spectral problem is solved using discrete inversion identities satisfied by these transfer matrices and functional Bethe ansatz methods. The resulting spectrum can be related to that of the XXZ spin-$1/2$ Heisenberg chain with boundary conditions depending on the topological sector of the anyon chain. The properties of this model in the critical regime are studied by finite size analysis of the spectrum. In particular, points in the phase diagram where the anyon chain realizes some of the rational ${\mathbb{Z}}_2$ orbifold theories are identified.

arXiv comment22 pages

References in corpus (17)

• Anyons in an exactly solved model and beyond
• An RVB phase in the triangular lattice quantum dimer model
• Interacting anyons in topological quantum liquids: The golden chain
• Condensate induced transitions between topologically ordered phases
• Fractionalization in an Easy-axis Kagome Antiferromagnet
• Collective States of Interacting Anyons, Edge States, and the Nucleation of Topological Liquids
• Anyonic quantum spin chains: Spin-1 generalizations and topological stability
• Exact solution and interfacial tension of the six-vertex model with anti-periodic boundary conditions
• Collective states of interacting Fibonacci anyons
• Non-Abelian anyons: when Ising meets Fibonacci
• The XXZ model with anti-periodic twisted boundary conditions
• Integrable anyon chains: from fusion rules to face models to effective field theories
• From spin to anyon notation: The XXZ Heisenberg model as a $D_3$ (or $su(2{)}_4$) anyon chain
• Quantum phases of a chain of strongly interacting anyons
• The $D(D_3)$-anyon chain: integrable boundary conditions and excitation spectra
• Inversion identities for inhomogeneous face models
• Non-Abelian $SU(3{)}_k$ anyons: inversion identities for higher rank face models

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• From the XXZ chain to the integrable Rydberg-blockade ladder via non-invertible duality defects
• Critical lines and ordered phases in a Rydberg-blockade ladder
• ${\mathbf{Z}}_n$ clock models and chains of $so(n{)}_2$ non-Abelian anyons: symmetries, integrable points and low energy properties
• Elaborating the phase diagram of spin-1 anyonic chains
• Dualities between 2+1d fusion surface models from braided fusion categories
• Signatures of non-Abelian anyons in the thermodynamics of an interacting fermion model
• Condensates of interacting non-Abelian $SO(5{)}_{N_f}$ anyons
• Condensation of non-Abelian $SU(3{)}_{N_f}$ anyons in a one-dimensional fermion model