Quantum Inverse Scattering Method with anyonic grading

TL;DR

This paper extends the Quantum Inverse Scattering Method to anyonic grading, enabling the construction of integrable models for interacting hard-core anyons and deriving their energy spectra via a generalized algebraic Bethe ansatz.

Contribution

It introduces a general framework for anyonic grading in the Quantum Inverse Scattering Method and constructs new integrable models like the anyonic t-J model.

Findings

Reconstructed the known hard core anyon model from the XXX model.

Derived the energy spectrum using a generalized algebraic Bethe ansatz.

Identified sector-dependent phase factors in the Bethe equations due to 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.