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arXiv:2209.05919 · Physical Review Research

Thermal Ising transition in two-dimensional SU(3) Fermi lattice gases with population imbalance

Hayato Motegi, Giacomo Marmorini, Nobuo Furukawa, Daisuke Yamamoto

Published Jun 20, 2023• 2 citations
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Abstract

We focus on three-component SU(3) Fermi gases loaded into a square optical lattice, with population imbalance between one component and the others.At strong coupling the system is described by the SU(3) Heisenberg model with an external field that couples to the population imbalance.We discuss the ground state at the mean-field level and then analyze the thermal fluctuations with the semiclassical Monte Carlo method.The interplay of interactions, population imbalance, and thermal fluctuations gives rise to a phase transition linked to the breaking of an emergent Ising symmetry, despite the absence of frustration.This represents another scenario of discrete symmetry breaking in low-dimensional systems with continuous symmetries.Possible implementations with cold alkaline-earth(-like) atoms are discussed.

DOI
10.1103/physrevresearch.5.l022056

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We focus on three-component SU(3) Fermi gases loaded into a square optical lattice, with population imbalance between one component and the others.At strong coupling the system is described by the SU(3) Heisenberg model with an external field that couples to the population imbalance.We discuss the ground state at the mean-field level and then analyze the thermal fluctuations with the semiclassical Monte Carlo method.The interplay of interactions, population imbalance, and thermal fluctuations gives rise to a phase transition linked to the breaking of an emergent Ising symmetry, despite the absence of frustration.This represents another scenario of discrete symmetry breaking in low-dimensional systems with continuous symmetries.Possible implementations with cold alkaline-earth(-like) atoms are discussed.
We study two-component (or pseudo-spin-12\frac{1}{2}21​) Bose or Fermi gases in one dimension, in which particles are convertible between the components. Through bosonization and numerical analyses of a simple lattice model, we demonstrate that, in such gases, a strong intercomponent repulsion induces spontaneous population imbalance between the components, namely, the ferromagnetism of the pseudo spins. The imbalanced phase contains gapless charge excitations characterized as a Tomonaga-Luttinger liquid and gapped spin excitations. We uncover a crucial effect of the intercomponent particle hopping on the transition to the imbalanced phase. In the absence of this hopping, the transition is of first order. At the transition point, the energy spectrum reveals certain degeneracy indicative of an emergent SU(2)\text{SU}(2)SU(2) symmetry. With an infinitesimal intercomponent hopping, the transition becomes of Ising type. We determine the phase diagram of the model accurately and test the reliability of the weak-coupling bosonization formalism.
We study the quantum and thermal phase transition phenomena of the SU(3) Heisenberg model on triangular lattice in the presence of magnetic fields. Performing a scaling analysis on large-size cluster mean-field calculations endowed with a density-matrix renormalization-group solver, we reveal the quantum phases selected by quantum fluctuations from the massively degenerate classical ground-state manifold. The magnetization process up to saturation reflects three different magnetic phases. The low- and high-field phases have strong nematic nature, and especially the latter is found only via a nontrivial reconstruction of symmetry generators from the standard spin and quadrupolar description. We also perform a semiclassical Monte Carlo simulation to show that thermal fluctuations prefer the same three phases as well. Moreover, we find that exotic topological phase transitions driven by the binding-unbinding of fractional (half-)vortices take place, due to the nematicity of the low- and high-field phases. Possible experimental realization with alkaline-earth-like cold atoms is also discussed.
Pairing in a population-imbalanced Fermi system in a two-dimensional optical lattice is studied using determinant quantum Monte Carlo simulations and mean-field calculations. The approximation-free numerical results show a wide range of stability of the Fulde-Ferrell-Larkin-Ovchinnikov phase. Contrary to claims of fragility with increased dimensionality, we find that this phase is stable across a wide range of values for the polarization, temperature, and interaction strength. Both homogeneous and harmonically trapped systems display pairing with finite center-of-mass momentum, with clear signatures either in momentum space or real space, which could be observed in cold-atomic gases loaded in an optical lattice. We also use the harmonic level basis in the confined system and find that pairs can form between particles occupying different levels, which can be seen as the analog of the finite center-of-mass momentum pairing in the translationally invariant case. Finally, we perform mean-field calculations for the uniform and confined systems and show the results to be in good agreement with quantum Monte Carlo. This leads to a simple picture of the different pairing mechanisms, depending on the filling and confining potential.
We study the ground-state phase diagram of population balanced and imbalanced ultracold atomic Fermi gases with a short-range attractive interaction throughout the crossover from BCS to Bose-Einstein condensation (BEC), in a two-dimensional (2D) optical lattice comprised of a 2D array of 1D lines. We find that the mixing of lattice and continuum dimensions, together with population imbalance, has an extraordinary effect on pairing and the superfluidity of atomic Fermi gases. In the balanced case, the superfluid ground state prevails over the majority of the phase space. However, for relatively small lattice hopping integral ttt and large lattice constant ddd, a pair density wave (PDW) emerges unexpectedly at intermediate coupling strength, and the nature of the in-plane and overall pairing changes from particlelike to holelike in the BCS and unitary regimes, associated with an abnormal increase in the Fermi volume with the pairing strength. In the imbalanced case, the stable polarized superfluid phase shrinks to only a small portion of the entire phase space spanned by t,dt, dt,d, imbalance ppp, and interaction strength UUU, mainly in the bosonic regime of low ppp, moderately strong pairing, relatively large ttt, and small ddd. Due to the Pauli exclusion between paired and excessive fermions within the confined momentum space, a PDW phase emerges and the overall pairing evolves from particlelike into holelike, as the pairing strength grows stronger in the BEC regime. In both cases, the ground-state property is largely governed by the Fermi surface topology. These findings are very different from the cases of a pure 3D continuum, a 3D lattice, or a 1D optical lattice.
We review recent experimental and theoretical progress on ultracold alkaline-earth Fermi gases with emergent SU(N) symmetry. Emphasis is placed on describing the ground-breaking experimental achievements of recent years. The latter include (1) the cooling to below quantum degeneracy of various isotopes of ytterbium and strontium, (2) the demonstration of optical Feshbach resonances and the optical Stern-Gerlach effect, (3) the realization of a Mott insulator of (173)Yb atoms, (4) the creation of various kinds of Fermi-Bose mixtures and (5) the observation of many-body physics in optical lattice clocks. On the theory side, we survey the zoo of phases that have been predicted for both gases in a trap and loaded into an optical lattice, focusing on two and three dimensional systems. We also discuss some of the challenges that lie ahead for the realization of such phases such as reaching the temperature scale required to observe magnetic and more exotic quantum orders. The challenge of dealing with collisional relaxation of excited electronic levels is also discussed.
The advent of ultracold alkaline-earth atoms in optical lattices has established a platform for investigating correlated quantum matter with SU(NNN) symmetry, offering highly tunable model parameters that allow experiments to access phenomena that are unavailable in conventional materials. Understanding the ground-state physics of SU(NNN) Fermi-Hubbard models away from the Heisenberg limit and from the spin-flavor balanced setting is important, as examining the flavor imbalance reveals new physics in Fermi-Hubbard models and shows how SU(NNN) phases react to practical experimental imperfections in optical lattices. In this study, mean-field phase diagrams are presented for the unit-density SU(3) Fermi-Hubbard model at two sets of flavor densities, (13−δ,13+δ,13)\left(\tfrac{1}{3}-δ,\tfrac{1}{3}+δ,\tfrac{1}{3}\right)(31​−δ,31​+δ,31​) and (14−δ,14+δ,12)\left(\tfrac{1}{4}-δ,\tfrac{1}{4}+δ,\tfrac{1}{2}\right)(41​−δ,41​+δ,21​), with the flavor imbalance introduced as δδδ. Novel phases are identified at moderate interaction strengths for both densities and their robustness is investigated in the presence of flavor imbalance. Furthermore, we provide microscopic explanations of the phases found and their stability. Analysis of thermal ensembles of random mean-field solutions indicate that, at temperatures accessible in state-of-the-art cold atom experiments, some spin orders are hard for conventional scattering or local observable measurements to detect, but can be more accessible with quantum gas microscopy in optical lattice experiments. This work also shows that nesting and Mottness, intertwined in the usual SU(2) Hubbard model in stark contrast to generic materials, can be tuned in the SU(3) model and play distinct roles. The resulting phase diagrams not only deepen our understanding of SU(NNN) Fermi-Hubbard models but also inform future experimental search for new phases.