Transport Properties of a One-Dimensional Two-Component Quantum Liquid with Hyperbolic Interactions

TL;DR

This paper studies a one-dimensional two-component quantum liquid with hyperbolic interactions, deriving its properties and analyzing ground state gap behavior using conformal and integral equation methods.

Contribution

It introduces the sinh-cosh interaction model and connects it to a Heisenberg-Ising fluid, deriving key physical relations and analyzing gap dynamics.

Findings

Derived Luttinger liquid relations for the model

Connected the sinh-cosh model to a Heisenberg-Ising fluid

Analyzed ground state gap opening and closing as interaction varies

Abstract

We present an investigation of the sinh-cosh (SC) interaction model with twisted boundary conditions. We argue that, when unlike particles repel, the SC model may be usefully viewed as a Heisenberg-Ising fluid with moving Heisenberg-Ising spins. We derive the Luttinger liquid relation for the stiffness and the susceptibility, both from conformal arguments, and directly from the integral equations. Finally, we investigate the opening and closing of the ground state gaps for both SC and Heisenberg-Ising models, as the interaction strength is varied.