Exotic magnetic orders for high-spin ultracold fermions

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 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.

Breaking of SU(4) symmetry and interplay between strongly correlated phases in the Hubbard model

“…A number of theoretical approaches have been developed recently to understand the low-temperature physics in the SU(4)-symmetric and other relevant four-component Hubbard and Heisenberg models. In particular, significant progress has been made in recent studies by quantum Monte Carlo (QMC) methods [13,[15][16][17][18], dynamical mean-field theory (DMFT) [19][20][21][22][23], one-dimensional approaches [24,25], high-temperature series expansion [26], and other mean-field approaches [27][28][29].…”

Order by disorder in a four-flavor Mott insulator on the fcc lattice

“…29 In ladder, 30 checkerboard lattice, 31 and honeycomb lattice with first and second neighbor exchange 32 the spins form SU(4) singlets or plaquettes, resulting in a translational symmetrybreaking states. In the square lattice, the proposals range from plaquettes, 21,33 via liquid, 34 to a dimerized state. 35 The SU(4) Heisenberg model in three-dimensional lattices is largely unexplored, with the exception of the cubic lattice, where a resonating plaquette state is suggested in Refs.…”

Mott insulators of ultracold fermionic alkaline earth atoms in three dimensions

“…While N -component such systems do not generically obey SU (N ) spin symmetry, the symmetry is enhanced above SU (2), 68 and such systems have received significant attention. [68][69][70][71][72][73][74] In Sec. II, we review the large-N solution to our model.…”