Collective dispersion relations for the 1D interacting two-component Bose and Fermi gases

TL;DR

This paper analyzes the elementary excitations in one-dimensional two-component Bose and Fermi gases using Bethe ansatz, providing analytic results in strong and weak interaction limits and confirming previous thermodynamic limit findings.

Contribution

It offers new analytic expressions for dispersion relations in limiting interaction regimes, enhancing understanding of 1D quantum gases.

Findings

Derived analytic dispersion relations for strong and weak interactions.

Confirmed previous Bethe ansatz results in the thermodynamic limit.

Provided insights into charge and spin excitations in 1D gases.

Abstract

We investigate the elementary excitations of charge and spin degrees for the 1D interacting two-component Bose and Fermi gases by means of the discrete Bethe ansatz equations. Analytic results in the limiting cases of strong and weak interactions are derived, where the Bosons are treated in the repulsive and the fermions in the strongly attractive regime. We confirm and complement results obtained previously from the Bethe ansatz equations in the thermodynamic limit.