Mesoscopic BCS pairing in the repulsive 1d-Hubbard model

TL;DR

This paper explores mesoscopic pairing phenomena in the 1D repulsive Hubbard model, revealing a BCS-like arrangement of spins and a connection to the Bethe ansatz solutions, highlighting novel pairing mechanisms.

Contribution

It demonstrates a novel mesoscopic pairing mechanism in the 1D Hubbard model by comparing Bethe ansatz equations and introducing a density-dependent phase-correlation.

Findings

Hubbard spin degrees form a BCS-like state

Cooper pairs form an un-condensed liquid on a lattice

Hubbard excitations are spin singlet seas

Abstract

We study mesoscopic pairing in the one dimensional repulsive Hubbard model and its interplay with the BCS model in the canonical ensemble. The key tool is comparing the Bethe ansatz equations of the two models in the limit of small Coulomb repulsion. For the ordinary Hubbard interaction the BCS Bethe equations with infinite pairing coupling are recovered; a finite pairing is obtained by considering a further density-dependent phase-correlation in the hopping amplitude of the Hubbard model. We find that spin degrees of freedom in the Hubbard ground state are arranged in a state of the BCS type, where the Cooper-pairs form an un-condensed liquid on a ``lattice'' of single particle energies provided by the Hubbard charge degrees of freedom; the condensation in the BCS ground state corresponds to Hubbard excitations constituted by a sea of spin singlets.