Unconventional pairing phases in the two-dimensional attractive Hubbard model with population imbalance

TL;DR

This study investigates the phase diagram of the two-dimensional attractive Hubbard model with population imbalance, revealing the prevalence of FFLO phases and limitations of traditional methods, with implications for related repulsive models.

Contribution

It introduces a linear programming approach to exactly impose population imbalance, uncovering unconventional pairing phases not accessible with standard methods.

Findings

FFLO phase is the ground state over a wide parameter range

Phase separation is limited to small population imbalances

Results relate to a particle-hole condensate in the repulsive Hubbard model

Abstract

The ground state phase diagram of the two-dimensional attractive Hubbard model with population imbalance is explored using a mean field ansatz. A linear programming algorithm is used to identify the blocked states, such that the population imbalance can be imposed exactly. This allows to explore regions of the number-projected phase diagram that can not be obtained with the conventional Bogoliubov-de Gennes ansatz. The Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) phase of pairs with non-zero momentum is found to be the ground state over a wide range of parameters, while phase separation occurs only in a limited region at small population imbalance. Through a particle-hole transformation these results can be related to the underdoped repulsive Hubbard model, where the FFLO phase takes the form of a particle-hole condensate that exhibits a spontaneous restoration of spin symmetry.