Quantum Simulation of the Hubbard Model: The Attractive Route

TL;DR

This paper explores how an attractive Hubbard model realized with ultra-cold Fermi gases can simulate the phases of the repulsive Hubbard model, including Mott insulators and d-wave superfluids, offering a potentially easier experimental approach.

Contribution

It demonstrates a method to infer phases of the repulsive Hubbard model through observations in an attractive model using canonical transformations, highlighting advantages over direct simulation.

Findings

Mott insulator and antiferromagnetic phases are more observable as paired and superfluid phases in the attractive model.

D-wave superfluid phase in the repulsive model corresponds to a d-wave antiferromagnetic phase in the attractive model.

The approach offers technical advantages and discusses possible solutions to implementation challenges.

Abstract

We study the conditions under which, using a canonical transformation, the phases sought after for the repulsive Hubbard model, namely a Mott insulator in the paramagnetic and anti-ferromagnetic phases, and a putative d-wave superfluid can be deduced from observations in an optical lattice loaded with a spin-imbalanced ultra-cold Fermi gas with attractive interactions, thus realizing the attractive Hubbard model. We show that the Mott insulator and antiferromagnetic phase of the repulsive Hubbard model are in fact more easy to observe as a paired, and superfluid phase respectively, in the attractive Hubbard model. The putative d-wave superfluid phase of the repulsive Hubbard model doped away from half-filling is related to a d-wave antiferromagnetic phase for the attractive Hubbard model. We discuss the advantages of this approach to 'quantum simulate' the Hubbard model in an optical lattice over the approach that attempts to directly simulate the doped Hubbard model in the repulsive regime. We also point out a number of technical difficulties of the proposed approach and, in some cases, suggest possible solutions.