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

Abstract

We investigate spin-1/2 electrons with local Hubbard interaction and variable range hopping amplitudes which decay like~$\sinh(κ)/\sinh(κr)$. 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 $U_c(κ>0)=0^+$. The charge gap in the singular limit $κ=0$ opens when the interaction strength equals the bandwidth, $U_c(κ=0)=W >0$.