Exotic magnetic orders for high-spin ultracold fermions

¹ Research Institute for Solid State Physics and Optics - P. O. Box 49, H-1525 Budapest, Hungary, EU
² ICFO-Institut de Ciències Fotòniques, Mediterranean Technology Park - E-08860 Castelldefels (Barcelona), Spain, EU
³ ICREA-Institució Catalana de Recerca i Estudis Avançats - Lluis Companys 23, E-08010 Barcelona, Spain, EU

^a eszirmai@szfki.hu

Received: 14 October 2010
Accepted: 28 February 2011

Abstract

We study Hubbard models for ultracold bosonic or fermionic atoms loaded into an optical lattice. The atoms carry a high spin F> 1/2, and interact on site via strong repulsive Van der Waals forces. Making convenient rearrangements of the interaction terms, and exploiting their symmetry properties, we derive low-energy effective models with nearest-neighbor interactions, and their properties. We apply our method to F=3/2, and 5/2 fermions on two-dimensional square lattice at quarter, and 1/6 fillings, respectively, and investigate mean-field equations for repulsive couplings. We find for F=3/2 fermions that the plaquette state appearing in the highly symmetric SU(4) case does not require fine tuning, and is stable in an extended region of the phase diagram. This phase competes with an SU(2) flux state, that is always suppressed for repulsive interactions in the absence of external magnetic field. The SU(2) flux state has, however, lower energy than the plaquette phase, and stabilizes in the presence of weak applied magnetic field. For F=5/2 fermions a similar SU(2) plaquette phase is found to be the ground state without external magnetic field.