From spin to anyon notation: The XXZ Heisenberg model as a $D_3$ (or $su(2{)}_4$) anyon chain

Abstract

We discuss a relationship between certain one-dimensional quantum spin chains and anyon chains. In particular we show how the XXZ Heisenberg chain is realised as a $D_3$ (alternately $su(2{)}_4$) anyon model. We find the difference between the models lie primarily in choice of boundary condition.

13 pages

References in corpus (3)

• Interacting anyons in topological quantum liquids: The golden chain
• A short introduction to Fibonacci anyon models
• Microscopic models of interacting Yang-Lee anyons

Cited by in corpus (11)

• Anyonic quantum spin chains: Spin-1 generalizations and topological stability
• Dualities in one-dimensional quantum lattice models: topological sectors
• From the XXZ chain to the integrable Rydberg-blockade ladder via non-invertible duality defects
• Integrable anyon chains: from fusion rules to face models to effective field theories
• Critical lines and ordered phases in a Rydberg-blockade ladder
• Exact solution of the $D_3$ non-Abelian anyon chain
• The $D(D_3)$-anyon chain: integrable boundary conditions and excitation spectra
• ${\mathbf{Z}}_n$ clock models and chains of $so(n{)}_2$ non-Abelian anyons: symmetries, integrable points and low energy properties
• Anyonic Liquids in Nearly Saturated Spin Chains
• Non-Abelian $SU(3{)}_k$ anyons: inversion identities for higher rank face models
• Density matrices in integrable face models