We theoretically investigate, using nonperturbative strong correlation techniques, Mott-insulating phases and magnetic ordering of two-component fermions in a two-dimensional double-well optical lattice. At filling of two fermions per site, there are two types of Mott insulators, one of which is characterized by spin-1 antiferromagnetism below the N\'eel temperature. The superexchange interaction in this system is induced by the interplay between the interband interaction and the spin degree of freedom. A great advantage of the double-well optical lattice is that the magnetic quantum phase diagram and the N\'eel temperature can be easily controlled by tuning the orbital energy splitting of the two-level system. Particularly, the N\'eel temperature can be one order of magnitude larger than that in standard optical lattices, facilitating the experimental search for magnetic ordering in optical lattice systems.
We present the application of the
SU(N) spin-wave theory to spin-orbital Mott insulators whose ground states exhibit magnetic orders. When taking both spin and orbital degrees of freedom into account rather than projecting Hilbert space onto the Kramers doublet, which is the lowest spin-orbital locked energy levels, the
SU(N) spin-wave theory should take the place of the
SU(2) one due to the inevitable spin-orbital multipole exchange interactions. To implement the application, we introduce an efficient general local mean-field method, which involves all local fluctuations, and develop the
SU(N) linear spin-wave theory. Our approach is tested firstly by calculating the multipolar spin-wave spectra of the
SU(4) antiferromagnetic model. Then, we apply it to spin-orbital Mott insulators. It is revealed that the Hund's coupling would influence the effectiveness of the isospin-
1/2 picture when the spin-orbital coupling is not large enough. We further carry out the
SU(N) spin-wave calculations of two materials, $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$ and
Sr2IrO4, and find that the magnonic and spin-orbital excitations are consistent with experiments.
We investigate the spin and orbital correlations of a superexchange model with spin
S=1 and orbital
L=1 relevant for
5d4 transition-metal Mott insulators [O. N. Meetei et al., Phys. Rev. B 91, 054412 (2015)], using exact diagonalization and density matrix renormalization group (DMRG). For spin-orbit coupling $\ensuremath{\lambda}=0$, the orbitals are in an entangled state that is decoupled from the spins. We find two phases with increasing $\ensuremath{\lambda}$: (I) the
S2 phase with two peaks in the structure factor for $\ensuremath{\lambda}\ensuremath{\le}{\ensuremath{\lambda}}_{c1}\ensuremath{\approx}0.34J$ where
J is the ferromagnetic exchange; and, (II) the
S1 phase for ${\ensuremath{\lambda}}_{c1}<\ensuremath{\lambda}\ensuremath{\le}{\ensuremath{\lambda}}_{c2}\ensuremath{\approx}1.2J$ with emergent antiferromagnetic correlations. Both
S1 and
S2 phases are shown to exhibit power-law correlations, indicative of a gapless spectrum. Upon increasing $\ensuremath{\lambda}>{\ensuremath{\lambda}}_{c2}$ leads to a product state of local spin-orbital singlets that exhibit exponential decay of correlations, indicative of a gapped phase. We obtain insights into the phases from the well-known Uimin-Lai-Sutherland model in an external field that provides an approximate description of our model within mean-field theory.
The SU(4)-symmetric spin-orbital model on the honeycomb lattice was recently studied in connection to correlated insulators such as the
eg Mott insulator
Ba3CuSb2O9 and the insulating phase of magic-angle twisted bilayer graphene at quarter filling. Here we provide a unified discussion of these systems by investigating an extended model that includes the effects of Hund's coupling and anisotropic, orbital-dependent exchange interactions. Using a combination of mean-field theory, linear flavor-wave theory, and variational Monte Carlo, we show that this model harbors a quantum spin-orbital liquid over a wide parameter regime around the SU(4)-symmetric point. For large Hund's coupling, a ferromagnetic antiferro-orbital ordered state appears, while a valence-bond crystal combined with a vortex orbital state is stabilized by dominant orbital-dependent exchange interactions.
We theoretically investigate, using non-perturbative strong correlation techniques, Mott insulating phases and magnetic ordering of two-component fermions in a two-dimensional double-well optical lattice. At filling of two fermions per site, there are two types of Mott insulators, one of which is characterized by spin-1 antiferromagnetism below the Neel temperature. The super-exchange interaction in this system is induced by the interplay between the inter-band interaction and the spin degree of freedom. A great advantage of the double-well optical lattice is that the magnetic quantum phase diagram and the Neel temperature can be easily controlled by tuning the orbital energy splitting of the two-level system. Particularly, the Neel temperature can be one order of magnitude larger than that in standard optical lattices, facilitating the experimental search for magnetic ordering in optical lattice systems.
We generalize the mean-field theory for the spinless Bose-Hubbard model to account for the different types of superfluid phases that can arise in the spin-1 case. In particular, our mean-field theory can distinguish polar and ferromagnetic superfluids, Mott insulator, that arise at integer fillings at zero temperature, and normal Bose liquids into which the Mott insulators evolve at finite temperatures. We find, in contrast to the spinless case, that several of the superfluid-Mott insulator transitions are of first order at finite temperatures. Our systematic study yields rich phase diagrams that include first-order and second-order transitions and a variety of tricritical points. We discuss the possibility of realizing such phase diagrams in experimental systems.