Intertwined orders from symmetry projected wavefunctions of repulsively interacting Fermi gases in optical lattices

TL;DR

This paper explores unconventional phases in the repulsive Fermi-Hubbard model using energy minimization techniques, revealing intertwined spin, charge, and pairing orders in optical lattice simulations.

Contribution

It introduces a novel approach employing symmetry-projected wavefunctions to study complex correlated phases without assuming specific order parameters.

Findings

Intertwined spin, charge, and pair-density waves in a d-wave superfluid background.

Emergence of these phases from homogeneous states with spiral magnetism as doping increases.

Enhanced long-range d-wave pairing correlations observed.

Abstract

Unconventional strongly correlated phases of the repulsive Fermi-Hubbard model, which could be emulated by ultracold vapors loaded in optical lattices, are investigated by means of energy minimizations with quantum number projection before variation and without any assumed order parameter. In a tube-like geometry of optical plaquettes to realize the four-leg ladder Hubbard Hamiltonian, we highlight the intertwining of spin-, charge-, and pair-density waves embedded in a uniform d-wave superfluid background. As the lattice filling increases, this phase emerges from homogenous states exhibiting spiral magnetism and evolves towards a doped antiferromagnet. A concomitant enhancement of long-ranged d-wave pairing correlations is also found. Numerical tests of the approach for two-dimensional clusters are carried out, too.