Bariev model for correlated hopping with crystalline field splitting

Abstract

The Bethe Ansatz solution of the one-dimensional Bariev model for correlated hopping for two orbital and two spin degrees of freedom per site is used to study the evolution of the electron bands as a function of crystalline field splitting $\ensuremath{\Delta}.$ The formation of charge bound states (nonlocal Cooper pairs) leads to a charge sector with Fermi surface, while all other excitations are gapped in the absence of fields. The gap for the interband transitions is gradually closed with increasing $\ensuremath{\Delta}.$ Two critical fields ${\ensuremath{\Delta}}_{1}$ and ${\ensuremath{\Delta}}_{2}$ $({\ensuremath{\Delta}}_{1}<{\ensuremath{\Delta}}_{2})$ have to be distinguished. For two electrons per site the system is a one-component Luttinger liquid if $\ensuremath{\Delta}<{\ensuremath{\Delta}}_{1},$ a two-component Luttinger liquid for ${\ensuremath{\Delta}}_{1}<\ensuremath{\Delta}<{\ensuremath{\Delta}}_{2},$ and an insulator for $\ensuremath{\Delta}>{\ensuremath{\Delta}}_{2}.$ The critical behavior of superconducting fluctuations is also discussed.