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Zhongguo kexue. Wulixue Lixue Tianwenxue

Mott insulating states and their quantum phase transitions of interacting spin-3/2 ultracold fermionic atoms on optical lattices

GuangMing ZHANG, Hong-Hao Tu

Published Apr 1, 2011• 0 citations
Publisher

Abstract

We first introduce the ultracold atoms and the optical lattices. Then, we analyze various Mott insulating phases of interacting spin-3=2 fermionic ultracold atoms in two-dimensional square optical lattices. Using a generalized Hubbard model, we identify two distinct symmetry breaking phases: the spin-quadrupole ordering phase and the spin-dipole-spin-octupole ordering phase. Near the SU(4) symmetric point, we find that an algebraic spin liquid phase may emerge due to strong quantum fluctuations. Finally, the possible quantum phase transitions between these exotic phases are also discussed.

DOI
10.1360/132011-61

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We first introduce the ultracold atoms and the optical lattices. Then, we analyze various Mott insulating phases of interacting spin-3=2 fermionic ultracold atoms in two-dimensional square optical lattices. Using a generalized Hubbard model, we identify two distinct symmetry breaking phases: the spin-quadrupole ordering phase and the spin-dipole-spin-octupole ordering phase. Near the SU(4) symmetric point, we find that an algebraic spin liquid phase may emerge due to strong quantum fluctuations. Finally, the possible quantum phase transitions between these exotic phases are also discussed.
We study various Mott insulating phases of interacting spin-32\frac{3}{2}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.
Based on a generalized one-band Hubbard model, we study magnetic properties of Mott insulating states for ultracold spin-32\frac{3}{2}23​ fermionic atoms in optical lattices. When the sss-wave scattering lengths for the total spin S=2,0S=2,0S=2,0 satisfy conditions a2>a0>0{a}_{2}>{a}_{0}>0a2​>a0​>0, we apply a functional integral approach to the half filled case, where the spin-quadrupole fluctuations dominate. On a two-dimensional square lattice, the saddle-point solution yields a staggered spin-quadrupole ordering at zero temperature with symmetry breaking from SO(5) to SO(4). Both spin and spin-quadrupole static structure factors are calculated, displaying highly anisotropic spin antiferromagnetic fluctuations and antiferroquadrupole long-range correlations, respectively. When Gaussian fluctuations around the saddle point are taken into account, spin-quadrupole density waves with a linear dispersion are derived. Compared with the spin-density waves in the half filled spin-12\frac{1}{2}21​ Hubbard model, the quadrupole density wave velocity is saturated in the strong-coupling limit, and there are no transverse spin-quadrupole mode couplings, as required by the SO(4) invariance of the effective action. Finally, in the strong-coupling limit of the model Hamiltonian, we derive the effective hyperfine spin-exchange interactions for the Mott insulating phases in the quarter filled and half filled cases, respectively.
The interplay between charge and spin degrees of freedom in strongly correlated fermionic systems, in particular of Dirac fermions, is a long-standing problem in condensed matter physics. We investigate the competing orders in the half-filled SU(2N)\mathrm{SU}(2N)SU(2N) Hubbard model on a honeycomb lattice, which can be accurately realized in optical lattices with ultracold large-spin alkaline-earth fermions. Employing large-scale projector determinant quantum Monte Carlo simulations, we have explored quantum phase transitions from the gapless Dirac semimetals to the gapped Mott insulating phases in the SU(4) and SU(6) cases. Both of these Mott insulating states are found to be columnar valence bond solid (cVBS) and to be absent of the antiferromagnetic N\'eel ordering and the loop current ordering. Inside the cVBS phases, the dimer ordering is enhanced by increasing fermion components and behaves nonmonotonically as the interaction strength increases. Although the transitions generally should be of first order due to a cubic invariance possessed by the cVBS order, the coupling to gapless Dirac fermions can soften the transitions to second order through a nonanalytic term in the free energy. Our simulations provide important guidance for the experimental explorations of novel states of matter with ultracold alkaline-earth fermions.
Mott insulators with both spin and orbital degeneracy are pertinent to a large number of transition metal oxides. The intertwined spin and orbital fluctuations can lead to rather exotic phases such as quantum spin-orbital liquids. Here, we consider two-component (spin 1/2) fermionic atoms with strong repulsive interactions on the p band of the optical square lattice. We derive the spin-orbital exchange for quarter filling of the p band when the density fluctuations are suppressed, and show that it frustrates the development of long-range spin order. Exact diagonalization indicates a spin-disordered ground state with ferro-orbital order. The system dynamically decouples into individual Heisenberg spin chains, each realizing a Luttinger liquid accessible at higher temperatures compared to atoms confined to the s band.
We study the Mott phases and superfluid-insulator transition of spin-three bosons in an optical lattice with an anisotropic two-dimensional optical trap. We chart out the phase diagrams for Mott states with n=1n=1n=1 and n=2n=2n=2 atoms per lattice site. It is shown that the long-range dipolar interaction stabilizes a state where the chains of the ferromagnetically aligned spins run along the longer trap direction while the spin ordering is staggered between nearby chains, leading to an antiferromagnetic ordering along the shorter trap direction. We also obtain the mean-field phase boundary for the superfluid-insulator transition in these systems and study the nature of spin ordering in the superfluid state near the transition. We show that, inside the superfluid phase and near the superfluid-insulator phase boundary, the system undergoes a first-order antiferromagnetic-ferromagnetic spin ordering transition. We discuss implications of our results for 52Cr^{52}\mathrm{Cr}52Cr atoms and suggest possible experiments to detect different phases in such systems.
The suppression of antiferromagnetic ordering in geometrically frustrated Hubbard models leads to a variety of exotic quantum phases including quantum spin liquids and chiral states. Here, we focus on the Hubbard model on one of the simplest frustrated lattice geometries, a triangular lattice. Motivated by the recent realization of ultracold fermionic atoms in triangular optical lattices, we study the properties of the triangular-lattice Hubbard model through a numerical linked-cluster expansion algorithm. We investigate the Mott insulator transition finding a critical interaction Uc/t=7.0(2){U}_{c}/t=7.0(2)Uc​/t=7.0(2) and use spatial two- and three-point correlation functions to explore doped and imbalanced systems. Our results demonstrate that many interesting features occur at temperatures previously obtained for ultracold fermions in optical lattices and are accessible by upcoming experiments. Our calculations will be helpful for thermometry in ultracold atom quantum simulators and can guide experimental searches for exotic quantum phases in atomic triangular Hubbard quantum simulators.