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Low Temperature Physics

Explicit symmetry breaking and effective spin models for four-component interacting Fermi gases in lattice potentials

Vladyslav Unukovych, Stanislava Litvinova, Andrii Sotnikov

Published Jan 1, 2025• 0 citations
Publisher

Abstract

We study low-temperature properties of the four-component Fermi gas of neutral atoms in optical lattice for several cases of explicit breaking of the SU(4) pseudospin symmetry in the framework of the Fermi–Hubbard model. For a reduced two-site system, we analyze the energy states and effective magnetic couplings in cases, where four interacting spin flavors in the Hubbard Hamiltonian form the symmetry subgroups of the type “three by one” or “two by two” according to their tunneling and interaction amplitudes, independently, and study behavior of the corresponding effective Heisenberg models in the limit of strong interaction. We also obtain and analyze the spatial density distributions of spin components in a harmonic optical trap for each case of explicit symmetry breaking.

DOI
10.1063/10.0034554

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Abstract We study an SU(4)-symmetric ultracold fermionic mixture in a cubic optical lattice with a variable tunneling amplitude along one particular crystallographic axis in the crossover region from the two- to three-dimensional spatial geometry. To theoretically analyze the emerging magnetic phases and physical observables, we describe the system within the framework of the Fermi–Hubbard model and apply dynamical mean-field theory. We show that in two limiting cases of anisotropy, there are two phases with different antiferromagnetic orderings in the zero temperature limit and we determine a region of their coexistence. We also study the stability regions of different magnetically ordered states and density profiles of the gas in the harmonic optical trap.
We study the thermodynamic properties of four-component fermionic mixtures described by the Hubbard model using the dynamical mean-field-theory approach. Special attention is given to the system with SU(4)-symmetric interactions at half filling, where we analyze equilibrium many-body phases and their coexistence regions at nonzero temperature for the case of simple cubic lattice geometry. We also determine the evolution of observables in low-temperature phases while lowering the symmetry of the Hamiltonian towards the two-band Hubbard model. This is achieved by varying interflavor interactions or by introducing the spin-flip term (Hund's coupling). By calculating the entropy for different symmetries of the model, we determine the optimal regimes for approaching the studied phases in experiments with ultracold alkali and alkaline-earth-like atoms in optical lattices.
We investigate effects of pseudospin population imbalance on Mott phases in one-dimensional trapped two-component atomic Fermi gases loaded on optical lattices based on the repulsive Hubbard model in harmonic traps. By using the density-matrix renormalization-group method, we numerically calculate density profiles of each component and clarify the pseudospin magnetism. Consequently, we find that all the features from weakly imbalance to fully polarized cases are well described by S=1/2S=1/2S=1/2 antiferromagnetic Heisenberg chain under magnetic field. These results indicate that the Mott phases offer experimental stages for studying various interacting spin systems.
Quantum simulation of the XXZXXZXXZ model with a two-component Bose- or Fermi-Hubbard model based on a Mott insulator background has been widely used in the investigations of quantum magnetism with ultracold neutral atoms. In most cases, the diagonal spin-spin interaction is always accompanied by a large spin-exchange interaction which hinders the formation of long-range magnetic order at low temperature. Here, we show that the spin-exchange interaction can be strongly reduced in a Mott insulator of paired atoms, while the diagonal spin-spin interaction remains unaffected. Thus, the effective magnetic models become the exact quantum Ising models in a one-dimensional (1D) or two-dimensional (2D) lattice. Meanwhile, we analyzed an experimentally achievable three-component Fermi-Hubbard model of 6Li^{6}\mathrm{Li}6Li with two hyperfine levels of atoms paired in the lattice. We find the long-range antiferromagnetism of such a three-component Fermi-Hubbard model can be much stronger than that of a typical two-component Fermi-Hubbard model at low temperature. Our results may be useful for experimental investigations of the quantum phase transition and quantum criticality of the 1D and 2D quantum Ising models with ultracold neutral atoms.
We study low-temperature properties of atomic gases in trimerized optical kagom\'e lattices. The laser arrangements that can be used to create these lattices are briefly described. We also present explicit results for the coupling constants of the generalized Hubbard models that can be realized in such lattices. In the case of a single-component Bose gas the existence of a Mott insulator phase with fractional numbers of particles per trimer is verified in a mean-field approach. The main emphasis of the paper is on an atomic spinless interacting Fermi gas in the trimerized kagom\'e lattice with two fermions per site. This system is shown to be described by a quantum spin-1∕21∕21∕2 model on the triangular lattice with couplings that depend on the bond directions. We investigate this model by means of exact diagonalization. Our key finding is that the system exhibits nonstandard properties of a quantum spin-liquid crystal: it combines planar antiferromagnetic order in the ground state with an exceptionally large number of low-energy excitations. The possibilities of experimental verification of our theoretical results are critically discussed.
We investigate magnetic properties of strongly interacting four component spin-3/2 ultracold fermionic atoms in the Mott insulator limit with one particle per site in an optical lattice with honeycomb symmetry. In this limit, atomic tunneling is virtual, and only the atomic spins can exchange. We find a competition between symmetry-breaking and liquidlike disordered phases. Particularly interesting are valence bond states with bond centered magnetizations, situated between the ferromagnetic and conventional valence bond phases. In the framework of a mean-field theory, we calculate the phase diagram and identify an experimentally relevant parameter region where a homogeneous SU(4) symmetric Affleck-Kennedy-Lieb-Tasaki--like valence bond state is present.