One-dimensional two-component Bose gas and the algebraic Bethe ansatz

TL;DR

This paper applies the nested algebraic Bethe ansatz to a one-dimensional two-component Bose gas model with delta-function interactions, deriving Bethe vectors and a series representation of the monodromy matrix to analyze its properties.

Contribution

It introduces a lattice approximation approach to find Bethe vectors and provides a series representation of the monodromy matrix in terms of Bose fields for the continuous model.

Findings

Derived Bethe vectors for the two-component Bose gas model.

Obtained a series representation of the monodromy matrix in Bose fields.

Facilitated asymptotic analysis of the monodromy matrix over the spectral parameter.

Abstract

We apply the nested algebraic Bethe ansatz to a model of one-dimensional two-component Bose gas with delta-function repulsive interaction. Using a lattice approximation of the L-operator we find Bethe vectors of the model in the continuous limit. We also obtain a series representation for the monodromy matrix of the model in terms of Bose fields. This representation allows us to study an asymptotic expansion of the monodromy matrix over the spectral parameter.