Competing orders in one dimensional spin 3/2 fermionic systems

Novel competing orders are found in spin 3/2 cold atomic systems in one-dimensional optical traps and lattices. In particular, the quartetting phase, a four-fermion counterpart of Cooper pairing, exists in a large portion of the phase diagram. The transition between the quartetting and singlet Cooper pairing phases is controlled by an Ising symmetry breaking effect in one of the spin channels. The singlet Cooper pairing phase also survives in the purely repulsive interaction regime. In addition, various charge and bond ordered phases are identified at commensurate fillings in lattice systems.Comment: 4 pages, 2 figures, revised versio

Exotic many-body physics with large-spin Fermi gases

The experimental realization of quantum degenerate cold Fermi gases with large hyperfine spins opens up a new opportunity for exotic many-body physics

Resonating plaquette phases in large spin cold atom systems

Large spin cold atom systems can exhibit novel magnetic properties which do not appear in usual spin-1/2 systems. We investigate the SU(4) resonating plaquette state in the three dimensional cubic optical lattice with spin-3/2 cold fermions. A novel gauge field formalism is constructed to describe the Rokhsar-Kivelson type of Hamiltonian and a duality transformation is used to study the phase diagram. Due to the proliferation of topological defects, the system is generally gapped for the whole phase diagram of the quantum model, which agrees with the recent numerical studies. A critical line is found for the classical plaquette system, which also corresponds to a quantum many-body wavefunction in a "plaquette liquid phase".Comment: 6 pages, 3 figure

A Quantized Inter-level Character in Quantum Systems

For a quantum system subject to external parameters, the Berry phase is an intra-level property, which is gauge invariant module $2\pi$ for a closed loop in the parameter space and generally is non-quantized. In contrast, we define a inter-band character $\Theta$ for a closed loop, which is gauge invariant and quantized as integer values. It is a quantum mechanical analogy of the Euler character based on the Gauss-Bonnet theorem for a manifold with a boundary. The role of the Gaussian curvature is mimicked by the difference between the Berry curvatures of the two levels, and the counterpart of the geodesic curvature is the quantum geometric potential which was proposed to improve the quantum adiabatic condition. This quantized inter-band character is also generalized to quantum degenerate systems

Four-coloring model and frustrated superfluidity in the diamond lattice

We propose a novel four-coloring model which describes "frustrated superfluidity" of $p$-band bosons in the diamond optical lattice. The superfluid phases of the condensate wavefunctions on the diamond-lattice bonds are mapped to four distinct colors at low temperatures. The fact that a macroscopic number of states satisfy the constraints that four differently colored bonds meet at the same site leads to an extensive degeneracy in the superfluid ground state at the classical level. We demonstrate that the phase of the superfluid wavefunction as well as the orbital angular momentum correlations exhibit a power-law decay in the degenerate manifold that is described by an emergent magnetostatic theory with three independent flux fields. Our results thus provide a novel example of critical superfluid phase with algebraic order in three dimensions. We further show that quantum fluctuations favor a N\'eel ordering of orbital angular moments with broken sublattice symmetry through the order-by-disorder mechanism.Comment: 5 pages, 4 figures, and supplementary material