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arXiv:cond-mat/0703284 · Physical Review B

Mott insulating phases and quantum phase transitions of interacting spin- 32 fermionic cold atoms in optical lattices at half filling

Hong-Hao Tu, Guang-Ming Zhang, Lu Yu

Published Jul 31, 2007• 14 citations
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Abstract

We study various Mott insulating phases of interacting spin-$\frac{3}{2}$ 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.

DOI
10.1103/physrevb.76.014438

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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 \ensuremathπ\ensuremath{\pi}\ensuremathπ-flux phase may emerge due to strong quantum fluctuations, leading to spin algebraic correlations and gapless excitations.
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.
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.
We experimentally study the emergence of antiferromagnetic correlations between ultracold fermionic atoms in a two-dimensional optical lattice with decreasing temperature. We determine the uniform magnetic susceptibility of the two-dimensional Hubbard model from simultaneous measurements of the in situ density distribution of both spin components. At half filling and strong interactions our data approach the Heisenberg model of localized spins with antiferromagnetic correlations. Moreover, we observe a fast decay of magnetic correlations when doping the system away from half filling.
We discuss the appearance of quantum orders in the Hubbard model for interacting electrons, at half-filling. Such phases do not have local order parameters and need to be characterized by the quantum mechanical properties of their ground state. On one hand, we study the Mott transition from a metal to a spin liquid insulator in two dimensions, of potential relevance to some layered organic compounds. The correlation-driven transition occurs at fixed filling and involves fractionalization of the electron: upon entering the insulator, a Fermi surface of neutral spinons coupled to an internal gauge field emerges. We focus on the transport properties near the quantum critical point and find that the emergent gauge fluctuations play a key role in determining the universal scaling. Second, motivated by a class of three-dimensional transition metal oxides, the pyrochlore iridates, we study the interplay of non-trivial band topology and correlations. Building on the strong spin orbit coupling in these compounds, we construct a general microscopic Hubbard model and determine its mean-field phase diagram, which contains topological insulators, Weyl semimetals, axion insulators and various antiferromagnets. We also discuss the effects many-body correlations on theses phases. We close by examining a fractionalized topological insulator that combines the two main themes of the thesis: fractionalization and non-trivial band topology. Specifically, we study how the two-dimensional protected surface states of a topological Mott insulator interact with a three-dimensional emergent gauge field. Various correlation effects on observables are identified.
We investigate possible realizations of exotic SU(N)\mathrm{SU}(N)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)\mathrm{SU}(N)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 NNN, two distinct types of SPT phases: an orbital Haldane phase, analogous to a spin-N/2N/2N/2 Haldane phase, and a topological SU(N)\mathrm{SU}(N)SU(N) phase, which we fully characterize by its entanglement properties. We also propose sets of nonlocal order parameters that characterize the SU(N)\mathrm{SU}(N)SU(N) topological phases found here.