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arXiv:2403.04319 · Journal of Physics B Atomic Molecular and Optical Physics

Anisotropy-driven magnetic phase transitions in SU(4)-symmetric Fermi gas in three-dimensional optical lattices

Vladyslav Unukovych, Andrii Sotnikov

Published Aug 5, 2024• 2 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1088/1361-6455/ad6b63

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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.
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We theoretically address magnetic ordering at zero and finite temperature in both homogeneous and trapped Bose-Bose mixtures in optical lattices. By using bosonic dynamical mean-field theory, we obtain the phase diagram of the homogeneous two-component Bose-Hubbard model in a three-dimensional cubic lattice, which features competing magnetic order of XYXYXY ferromagnetic and antiferromagnetic type in addition to the Mott and superfluid states. We show that these magnetic phases persist also in the presence of a harmonic 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 study theoretically many-body equilibrium magnetic phases and corresponding thermodynamic characteristics of ultracold three-component fermionic mixtures in optical lattices described by the SU(3)-symmetric single-band Hubbard model. Our analysis is based on the generalization of the exact diagonalization solver for multicomponent mixtures that is used in the framework of the dynamical mean-field theory. It allows us to obtain a finite-temperature phase diagram with the corresponding transition lines to magnetically ordered phases at filling one particle per site (1/3 band filling) in simple cubic lattice geometry. Based on the developed theoretical approach, we also attain the necessary accuracy to study the entropy dependence in the vicinity of magnetically ordered phases that allows us to make important predictions for ongoing and future experiments aiming to approach and study long-range-order phases in ultracold atomic mixtures.
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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.