Quantum Inverse Scattering Method with anyonic grading

Abstract

We formulate the Quantum Inverse Scattering Method for the case of anyonic grading. This provides a general framework for constructing integrable models describing interacting hard-core anyons. Through this method we reconstruct the known integrable model of hard core anyons associated with the XXX model, and as a new application we construct the anyonic $t-J$ model. The energy spectrum for each model is derived by means of a generalisation of the algebraic Bethe ansatz. The grading parameters implementing the anyonic signature give rise to sector-dependent phase factors in the Bethe ansatz equations.

14 pages, revised version, some clarifications in text, references added and upated

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Cited by in corpus (15)

• Ground-state properties of hard-core anyons in one-dimensional optical lattices
• Dynamical properties of hard-core anyons in one-dimensional optical lattices
• Quantum Walks of Two Interacting Anyons in 1D Optical Lattices
• Classifying integrable spin-1/2 chains with nearest neighbour interactions
• One-particle density matrix of a trapped Lieb-Liniger anyonic gas
• Correlation functions of one-dimensional strongly interacting two-component gases
• Ground state properties of hard-core anyons in a harmonic potential
• One-Dimensional Impenetrable Anyons in Thermal Equilibrium. III. Large distance asymptotics of the space correlations
• One-Dimensional Impenetrable Anyons in Thermal Equilibrium. IV. Large Time and Distance Asymptotic Behavior of the Correlation Functions
• Non-equilibrium dynamics of the anyonic Tonks-Girardeau gas at finite temperature
• One-dimensional hard-core anyon gas in a harmonic trap at finite temperature
• Quantum Integrable 1D anyonic Models: Construction through Braided Yang-Baxter Equation
• Nonequilibrium dynamics in one-dimensional strongly interacting two-component gases
• Universal properties and dynamical bosonization of strongly interacting one-dimensional anyons
• Necessity of orthogonal basis vectors for the two-anyon problem in one-dimensional lattice