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arXiv:1304.7676 · Physical Review B

Competition between three-sublattice order and superfluidity in the quantum three-state Potts model of ultracold bosons and fermions on a square optical lattice

Laura Messio, Philippe Corboz, Frédéric Mila

Published Oct 4, 2013• 2 citations
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Abstract

We study a quantum version of the three-state Potts model that includes as special cases the effective models of bosons and fermions on the square lattice in the Mott-insulating limit. It can be viewed as a model of quantum permutations with amplitudes ${J}_{\ensuremath{\parallel}}$ and ${J}_{\ensuremath{\perp}}$ for identical and different colors, respectively. For ${J}_{\ensuremath{\parallel}}={J}_{\ensuremath{\perp}}>0$ it is equivalent to the SU(3) Heisenberg model, which describes the Mott-insulating phase of 3-color fermions, while the parameter range ${J}_{\ensuremath{\perp}}<\mathrm{min}(0,\ensuremath{-}{J}_{\ensuremath{\parallel}})$ can be realized in the Mott insulating phase of 3-color bosonic atoms. Using linear flavor wave theory, infinite projected entangled-pair states (iPEPS), and continuous-time quantum Monte Carlo simulations, we construct the full $T=0$ phase diagram, and we explore the $T\ensuremath{\ne}0$ properties for ${J}_{\ensuremath{\perp}}<0$. For dominant antiferromagnetic ${J}_{\ensuremath{\parallel}}$ interactions, a three-sublattice long-range ordered stripe state is selected out of the ground-state manifold of the antiferromagnetic Potts model by quantum fluctuations. Upon increasing $|{J}_{\ensuremath{\perp}}|$, this state is replaced by a uniform superfluid for ${J}_{\ensuremath{\perp}}<0$, and by an exotic three-sublattice superfluid followed by a two-sublattice superfluid for ${J}_{\ensuremath{\perp}}>0$. The transition out of the uniform superfluid (that can be realized with bosons) is shown to be a peculiar type of Kosterlitz-Thouless transition with three types of elementary vortices.

DOI
10.1103/physrevb.88.155106

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SU(N) Hubbard models exhibit a rich variety of phases, which may be realized through quantum simulation with ultracold atomic gases in optical lattices. In this work we study the Mott insulating phases of the SU(3) Hubbard model at 1/3-filling using infinite projected entangled-pair states, optimized with both imaginary time evolution and variational optimization. In the limit of strong interactions we reproduce the antiferromagnetic 3-sublattice ordered state previously identified in the SU(3) Heisenberg model. At intermediate interaction strength we find antiferromagnetic states exhibiting zigzag patterns of different lengths, in agreement with previous Hartree-Fock and constrained-path auxiliary-field quantum Monte Carlo calculations. We study the color order parameter and energy anisotropy, which are discontinuous across the phase transitions. Finally, we analyze the different energy contributions in two competing phases, identifying low-energy bonds at the corners of the zigzag that help stabilize the zigzag states.
Combining a semiclassical analysis with exact diagonalizations, we show that the ground state of the SU(3) Heisenberg model on the square lattice develops three-sublattice long-range order. This surprising pattern for a bipartite lattice with only nearest-neighbor interactions is shown to be the consequence of a subtle quantum order-by-disorder mechanism. By contrast, thermal fluctuations favor two-sublattice configurations via entropic selection. These results are shown to extend to the cubic lattice, and experimental implications for the Mott-insulating states of three-flavor fermionic atoms in optical lattices are discussed.
The superfluid--Mott-insulator phase transition of ultracold spin-1 bosons with ferromagnetic and antiferromagnetic interactions in an optical lattice is theoretically investigated. Two counterpropagating linearly polarized laser beams with the angle $\ensuremath{\theta}$ between the polarization vectors ($\mathrm{lin}\text{\ensuremath{-}}\ensuremath{\theta}\text{\ensuremath{-}}\mathrm{lin}$ configuration), driving an Fg=1{F}_{g}=1Fg​=1 to Fe=1{F}_{e}=1Fe​=1 internal atomic transition, create the optical lattice and at the same time couple atomic ground states with magnetic quantum numbers $m=\ifmmode\pm\else\textpm\fi{}1$. Due to the coupling the system can be described as a two-component one. At $\ensuremath{\theta}=0$ the system has a continuous isospin symmetry, which can be spontaneously broken, thereby fixing the number of particles in the atomic components. The phase diagram of the system and the spectrum of collective excitations, which are density waves and isospin waves, are worked out. In the case of ferromagnetic interactions, the superfluid--Mott-insulator phase transition is always second order, but in the case of antiferromagnetic interactions for some values of system parameters it is first order and the superfluid and Mott phases can coexist. Varying the angle $\ensuremath{\theta}$ one can control the populations of atomic components and continuously turn on and tune their asymmetry.
SU(N)\mathrm{SU}(N)SU(N) symmetric fermions on a lattice, which can be realized in ultracold-atom-based quantum simulators, have very promising prospects for realizing exotic states of matter. Here we present the ground-state phase diagram of the repulsive SU(3) Hubbard model on a honeycomb lattice at 1/3 filling obtained from infinite projected entangled pair states tensor network calculations. In the strongly interacting limit the ground state has plaquette order. Upon decreasing the interaction strength U/tU/tU/t we find a first-order transition at U/t=7.2(2)U/t=7.2(2)U/t=7.2(2) into a dimerized, color-ordered state, which extends down to U/t=4.5(5)U/t=4.5(5)U/t=4.5(5), at which the Mott transition occurs and the ground state becomes uniform. Our results may serve as a prediction and benchmark for future quantum simulators of SU(3) fermions.
We investigate the pairing symmetry of the superfluid state in repulsively interacting three-component (color) fermionic atoms in optical lattices. When two of the three color-dependent repulsions are much stronger than the other, pairing symmetry is an extended sss wave, although the superfluid state appears adjacent to the paired Mott insulator in the phase diagram. On the other hand, when two of the three color-dependent repulsions are weaker than the other, pairing symmetry is a ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ wave. This change in pairing symmetry is attributed to the change in the dominant quantum fluctuations from the density fluctuations of unpaired atoms and the color-density wave fluctuations to the color-selective antiferromagnet fluctuations. This phenomenon can be studied using existing experimental techniques.
We study, using quantum Monte Carlo (QMC) simulations, the ground state properties of spin-1 bosons trapped in a square optical lattice. The phase diagram is characterized by the mobility of the particles (Mott insulating or superfluid phase) and by their magnetic properties. For ferromagnetic on-site interactions, the whole phase diagram is ferromagnetic and the Mott insulators-superfluid phase transitions are second order. For antiferromagnetic on-site interactions, spin nematic order is found in the odd Mott lobes and in the superfluid phase. Furthermore, the superfluid-insulator phase transition is first or second order depending on whether the density in the Mott is even or odd. Inside the even Mott lobes we observe a singlet-to-nematic transition for certain values of the interactions. This transition appears to be first order.