Fermions with attractive interactions on optical lattices and implications for correlated systems

TL;DR

This paper investigates the superfluid transition temperature in the attractive Hubbard model across all fillings and interaction strengths, revealing a vanishing $T_c$ near strong coupling and suggesting a quantum critical transition.

Contribution

It provides a systematic analysis of pairing fluctuations in the attractive Hubbard model, highlighting differences from jellium and proposing a new superfluid phase at strong coupling.

Findings

$T_c$ vanishes at strong coupling near half filling.

The BEC limit differs significantly from jellium due to inter-site repulsion.

A phase diagram for d-wave pairing shows $T_c$ vanishes when $T^*$ is large.

Abstract

In this paper we address the behavior of the superfluid transition temperature $T_c$ in the attractive Hubbard model. We study systematically the effects of pairing fluctuations and address all filling fractions over the entire range of attractive interaction strength. While the attractive Hubbard model can be regarded as the generalization of BCS to Bose Einstein condensation (BEC) crossover to a lattice, we find that the BEC limit of this Hubbard model is very different from that of jellium, owing to the strong inter-site repulsion between pairs, which becomes important near half filling when the on-site attraction is strong. A central conclusion of our work is that in a lattice, around half filling, the smooth evolution from the BCS to the BEC limits is interrupted. For the attractive Hubbard model, $T_c$ vanishes when the system approaches the bosonic regime with increasing interaction strength. We suggest that the vanishing of $T_c$ at strong coupling strength may signal a quantum critical transition to another form of superfluid not continuously connected to a BCS-like phase. We present a simple variational ansatz for the ground state in this more strongly coupled superfluid. We further generalize the (s-wave) Hubbard model to d-wave pairing and address issues of potential relevance to high temperature superconductors. For the d-wave case, we present a phase diagram and show that here too, one observes a vanishing of $T_c$ when the pairing onset temperature $T^*$ becomes sufficiently large. We suggest that future experiments on ultracold fermions in optical lattices should not be exclusively limited to the repulsive Hubbard model, but should address the attractive model in order to elucidate features of high temperature superconductivity.