The phase diagram of spin-
3∕2 fermionic cold atoms trapped in a one-dimensional optical lattice is investigated at quarter filling (one atom per site) by means of large-scale numerical simulations. In full agreement with a recent low-energy approach, we find two phases with confined and deconfined Cooper pairs separated by an Ising quantum phase transition. The leading instability in the confined phase is an atomic-density wave with subdominant quartet superfluid instability made of four fermions. Finally, we reveal the existence of a bond-ordered Mott insulating phase in some part of the repulsive regime.
We investigate possible realizations of exotic
SU(N) symmetry-protected topological (SPT) phases with alkaline-earth cold fermionic atoms loaded into one-dimensional optical lattices. A thorough study of two-orbital generalizations of the standard
SU(N) Fermi-Hubbard model, directly relevant to recent experiments, is performed. Using state-of-the-art analytical and numerical techniques, we map out the zero-temperature phase diagrams at half-filling and identify several Mott-insulating phases. While some of them are rather conventional (nondegenerate, charge-density wave, or spin-Peierls-like), we also identify, for even
N, two distinct types of SPT phases: an orbital Haldane phase, analogous to a spin-
N/2 Haldane phase, and a topological
SU(N) phase, which we fully characterize by its entanglement properties. We also propose sets of nonlocal order parameters that characterize the
SU(N) topological phases found here.
The phase diagram of one-dimensional alkaline-earth fermionic atoms and ytterbium 171 atoms is investigated by means of a low-energy approach and density-matrix renormalization group calculations. For incommensurate filling, four gapless phases with a spin gap are found and consist of two superconducting instabilities and two coexisting bond and charge density-waves instabilities. In the half-filled case, seven Mott-insulating phases arise with the emergence of four non-degenerate phases with exotic hidden orderings.
We study the two-band model of spinless fermions in one dimension for weak repulsive interactions. In this case, the model is equivalent to the weakly interacting spinless two-leg ladder. We obtain nonuniversal analytic expressions for the power-law decays $\ensuremath{\propto}{x}^{\ensuremath{-}\ensuremath{\gamma}}$ of the charge-density and $\ensuremath{\propto}{x}^{\ensuremath{-}1/\ensuremath{\gamma}}$ of the superconducting pairing correlation functions. To leading order in the doping $\ensuremath{\delta}$ away from half filling and ${t}_{\ensuremath{\perp}}/t,$ we find $\ensuremath{\gamma}=1+({\ensuremath{\pi}}^{2}{/8)(t}_{\ensuremath{\perp}}{/t)}^{2}{\ensuremath{\delta}}^{2}$
(t and ${t}_{\ensuremath{\perp}}$ are the hopping terms along and between the chains), such that superconducting pairing correlations dominate. We furthermore show that the transition from the superconducting phase to the usual one-dimensional (Luttinger) metal occurs via a mixed phase, where superconducting pairs are formed in the bonding band only. We give the phase diagram as a function of temperature and doping.
We study the phase diagram of the extended Hubbard model on a two-dimensional square lattice, including on-site (
U) and nearest-neighbor (
V) interactions, at weak couplings. We show that the charge-density wave phase that is known to occur at half filling when
4V>U gives way to a
dxy-wave superconducting instability away from half filling, when the Fermi surface is not perfectly nested, and for sufficiently large repulsive
V and a range of on-site repulsive interaction
U. In addition, when nesting is further suppressed and in the presence of a nearest-neighbor attraction, a triplet time-reversal breaking
(px+ipy)-wave pairing instability emerges, competing with the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ pairing state that is known to dominate at fillings just slightly away from half. At even smaller fillings, where the Fermi surface no longer presents any nesting, the
(px+ipy)-wave superconducting phase dominates in the whole regime of on-site repulsions and nearest-neighbor attractions, while
dxy pairing occurs in the presence of on-site attraction. Our results suggest that zero-energy Majorana fermions can be realized on a square lattice in the presence of a magnetic field. For a system of cold fermionic atoms on a two-dimensional square optical lattice, both an on-site repulsion and a nearest-neighbor attraction would be required, in addition to rotation of the system to create vortices. We discuss possible ways of experimentally engineering the required interaction terms in a cold atom system.
We study various Mott insulating phases of interacting spin-
23 fermionic ultracold atoms in two-dimensional square optical lattices at half filling. Using a generalized one-band Hubbard model with hidden SO(5) symmetry, we identify two distinct symmetry breaking phases: the degenerate antiferromagnetic spin-dipole--spin-octupole ordering and spin-quadrupole ordering, depending on the sign of the spin-dependent interaction. These two competing orders exhibit very different symmetry properties, low energy excitations, and topological characterizations. Near the SU(4) symmetric point, a quantum critical state with a $\ensuremath{\pi}$-flux phase may emerge due to strong quantum fluctuations, leading to spin algebraic correlations and gapless excitations.