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

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(parallel to) and J(perpendicular to) for identical and different colors, respectively. For J(parallel to) = J(perpendicular to) > 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(perpendicular to) < min(0, - J(parallel to)) 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 not equal 0 properties for J(perpendicular to) < 0. For dominant antiferromagnetic J(parallel to) interactions, a three-sublattice long-range ordered stripe state is selected out of the ground-statemanifold of the antiferromagnetic Potts model by quantum fluctuations. Upon increasing vertical bar J(perpendicular to)vertical bar, this state is replaced by a uniform superfluid for J(perpendicular to) < 0, and by an exotic three-sublattice superfluid followed by a two-sublattice superfluid for J(perpendicular to) > 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.

Linear flavor-wave theory for fully antisymmetric SU( N ) irreducible representations

Francisco Hyunkyu Kim, Frédéric Mila, Pierre Marcel Nataf, Karlo Penc

The extension of the linear flavor-wave theory to fully antisymmetric irreducible representations (irreps) of SU(N) is presented in order to investigate the color order of SU(N) antiferromagnetic Heisenberg models in several two-dimensional geometries. The square, triangular, and honeycomb lattices are considered with m fermionic particles per site. We present two different methods: the first method is the generalization of the multiboson spin-wave approach to SU(N) which consists of associating a Schwinger boson to each state on a site. The second method adopts the Read and Sachdev bosons which are an extension of the Schwinger bosons that introduces one boson for each color and each line of the Young tableau. The two methods yield the same dispersing modes, a good indication that they properly capture the semiclassical fluctuations, but the first one leads to spurious flat modes of finite frequency not present in the second one. Both methods lead to the same physical conclusions otherwise: long-range Néel-type order is likely for the square lattice for SU(4) with two particles per site, but quantum fluctuations probably destroy order for more than two particles per site, with N=2m. By contrast, quantum fluctuations always lead to corrections larger than the classical order parameter for the tripartite triangular lattice (with N=3m) or the bipartite honeycomb lattice (with N=2m) for more than one particle per site, m>1, making the presence of color very unlikely except maybe for m=2 on the honeycomb lattice, for which the correction is only marginally larger than the classical order parameter.

2017

Quadrupolar Ordering in Two-Dimensional Spin-One Systems

Tamás András Tóth

The principal aim of this thesis is to gain a better understanding of the competition between magnetic and quadrupolar degrees of freedom on two-dimensional lattices. Recent experimental investigations of the material NiGa2S4 revealed several anomalous properties that might be accounted for within the framework of quadrupolar ordering. Exhibiting both a ferroquadrupolar and an antiferroquadrupolar phase, the S = 1 bilinear-biquadratic Heisenberg model on the triangular lattice is a possible candidate for describing the low-temperature behaviour of the system. In this work, we put forward a more realistic model that includes single-ion anisotropy. We perform a thorough investigation of the variational phase diagram of this model and we show that it exhibits a variety of unconventional phases. We derive the excitation spectrum of the quadrupolar phases in the phase diagram and we point out that ferroquadrupolar order is particularly sensitive to the nature of anisotropy. Finally, we study quantum effects in the perturbative limit of large anisotropy and we argue that the non-trivial degeneracy of the mean-field solution is lifted by an emergent supersolid phase. We also discuss our results in the context of NiGa2S4. In the second part of the thesis, we aim at gaining an insight into the interplay between geometrical frustration and quadrupolar degrees of freedom by mapping out the phase diagram of the spin-one bilinear-biquadratic model on the square lattice. Our variational approach reveals a remarkable 1/2-magnetization plateau of mixed quadrupolar and magnetic character above the classically degenerate "semi-ordered" phase, and this finding is corroborated by exact diagonalization of finite clusters. "Order-by-disorder" phenomenon gives rise to a state featuring three-sublattice antiferroquadrupolar order below the plateau, which is truly surprising given the bipartite nature of the square lattice. We place particular emphasis on investigating the properties of the SU(3) Heisenberg model, which is shown to feature a subtle competition between quantum and thermal fluctuations. Our results suggest a suppression of two-sublattice Néel order in a finite window below the SU(3) point. Experimental implications for the Mott-insulating states of three-flavour fermionic atoms in optical lattices are discussed.

EPFL2011

Quantum Monte Carlo Study of a Resonant Bose-Fermi Mixture

Gianluca Bertaina, Elisa Fratini

We study a resonant Bose-Fermi mixture at zero temperature by using the fixed-node diffusion Monte Carlo method. We explore the system from weak to strong boson-fermion interaction, for different concentrations of the bosons relative to the fermion component. We focus on the case where the boson density nB is smaller than the fermion density nF, for which a first-order quantum phase transition is found from a state with condensed bosons immersed in a Fermi sea, to a Fermi-Fermi mixture of composite fermions and unpaired fermions. We obtain the equation of state and the phase diagram, and we find that the region of phase separation shrinks to zero for vanishing nB

2013

Quadrupolar Ordering in Two-Dimensional Spin-One Systems

Tamás András Tóth

EPFL2011