Asymptotic Bethe-Ansatz results for a Hubbard Chain with 1/sinh-Hopping

TL;DR

This paper derives asymptotic Bethe-Ansatz equations for a Hubbard chain with variable-range hopping decaying as sinh, revealing a metal-insulator transition at zero interaction for finite decay parameter and a charge gap opening at critical interaction when decay vanishes.

Contribution

It introduces a generalized Bethe-Ansatz framework for a Hubbard model with sinh-decaying hopping, analyzing the metal-insulator transition and charge gap formation.

Findings

Metal-insulator transition at zero interaction for finite decay parameter

Charge gap opens when interaction equals bandwidth at zero decay

Derived generalized Lieb-Wu integral equations for this model

Abstract

We investigate spin-1/2 electrons with local Hubbard interaction and variable range hopping amplitudes which decay like~$\sinh(\kappa)/\sinh(\kappa r)$. Assuming integrability the Asymptotic Bethe Ansatz approach allows us to derive the generalized Lieb-Wu integral equations from the two-particle phase shift. Due to the nesting property there is a metal-to-insulator transition at $U_c(\kappa>0)=0^+$. The charge gap in the singular limit $\kappa=0$ opens when the interaction strength equals the bandwidth, $U_c(\kappa=0)=W >0$.