The role of the multiorbital effects on the emergence of frustrated electronic orders on the triangular lattice at half filling is investigated through an extended spinless fermion Hubbard model. By using two complementary approaches, unrestricted Hartree-Fock and exact diagonalizations, we unravel a very rich phase diagram controlled by the strength of both local and off-site Coulomb interactions and by the interorbital hopping anisotropy ratio ${t}^{\ensuremath{'}}/t$. Three robust unconventional electronic phases, a pinball liquid, an inverse pinball liquid, and a large-unit-cell $\sqrt{12}\ifmmode\times\else\texttimes\fi{}\sqrt{12}$ droplet phase, are found to be generic in the triangular geometry, being controlled by the band structure parameters. The latter are also stabilized in the isotropic limit of our microscopic model, which recovers the standard SU(2) spinful extended single-band Hubbard model.
The ground-state phase diagrams of the three-orbital
t2g Hubbard model are studied using a Hartree-Fock approximation. First, a complete set of multipolar order parameters for
t2g models defined in terms of the effective total angular momentum
jeff is theoretically derived. These order parameters can classify off-diagonal orders between
jeff=1/2 and
jeff=3/2 manifolds. Second, through extensive Hartree-Fock calculations, the ground-state phase diagrams in the space of (1) the on-site Coulomb repulsion
U, (2) the spin-orbit coupling $\ensuremath{\lambda}$, and (3) the number of electrons
n are mapped out. A variety of nontrivial quantum phases with
jeff-diagonal and
jeff--off-diagonal multipole orders are found. Finally, future studies using more numerically expensive methods, such as dynamical mean-field theory, are discussed.
We consider an extended Hubbard model of interacting fermions on a lattice. The fermion kinetic energy corresponds to a tight-binding Hamiltonian with nearest-neighbor (-t) and next-nearest-neighbor (
t∣IH) hopping matrix elements. In addition to the on-site Hubbard interaction (U) we also consider a nearest-neighbor repulsion (V). We obtain the zero-temperature phase diagram of our model within the Hartree-Fock approximation. We consider ground states having charge- and spin-density-wave ordering as well as states with orbital antiferromagnetism or spin nematic order. The latter two states correspond to particle-hole binding with ${\mathrm{d}}_{{\mathrm{x}}^{2}\mathrm{\ensuremath{-}}{\mathrm{y}}^{2}}$ symmetry in the charge and spin channels, respectively. For
t∣IH=0, only the charge-density-wave and spin-density-wave states are energetically stable. For nonzero
t∣IH, we find that orbital antiferromagnetism (or spin nematic) order is stable over a finite portion of the phase diagram at weak coupling. This region of stability is seen to grow with increasing values of
t∣IH.
We study the phase diagram of the extended Hubbard model on the kagome lattice at 1/3 filling. By combining a configuration interaction approach to an unrestricted Hartree-Fock, we construct an effective Hamiltonian which takes the correlations back on top of the mean-field solution. We obtain a rich phase diagram with, in particular, the presence of two original phases. The first one consists of local polarized droplets of metal standing on the hexagons of the lattice and an enlarged kagome charge order, inversely polarized, on the remaining sites. The second, obeying a local ice-rule type constraint on the triangles of the kagome lattice, is driven by an antiferromagnetic coupling of spins and is constituted of disconnected six-spin singlet rings. The nature and stability of these phases at large interactions are studied via trial wave functions and perturbation theory.
Orbital degrees of freedom play an important role in understanding the emergence of unconventional quantum phases. Ultracold atomic gases in optical lattices provide a wonderful platform to simulate orbital physics. In this work, we consider spinless fermionic atoms loaded into
p-orbital bands of a two-dimensional frustrated triangular lattice. The system can be described by an extended Fermi-Hubbard model, which is numerically solved by using the orbital version of real-space dynamical mean-field theory. Due to the interplay of anisotropic hoppings and geometrical frustration, a rich phase diagram is found, including stripe-orbital, paraorbital, and ferro-orbital phases, in contrast to its bosonic analog with orbital-skyrmion ordering in the identical lattice. In order to understand the underlying mechanics of competing orbital orders, we derive an effective orbital-exchange model, which yields consistent explanation with our main numerical results.