We apply the dynamical mean-field approach to the four-component SU(4)-symmetric Fermi-Hubbard model to study transitions between different magnetically ordered phases as well as the hysteresis behavior in the unordered regime. At quarter filling (one particle per site) on the square lattice we identify both the two-sublattice and plaquette-ordered antiferromagnetic phases with the corresponding entropy-driven hierarchy for critical temperatures. We also analyze the behavior of thermodynamic characteristics: the local double occupancy, compressibility, and entropy per particle, which are relevant for experiments with ultracold alkaline-earth(-like) atoms in optical lattices.
We study finite-temperature properties of ultracold four-component mixtures of alkaline-earth-metal-like atoms in optical lattices that can be effectively described by the two-band spin-
1/2 Hubbard model including Hund's exchange coupling term. Our main goal is to investigate the effect of exchange interactions on finite-temperature magnetic phases for a wide range of lattice fillings. We use the dynamical mean-field theory approach and its real-space generalization to obtain finite-temperature phase diagrams including transitions to magnetically ordered phases. It allows to determine optimal experimental regimes for approaching long-range ferromagnetic ordering in ultracold gases. We also calculate the entropy in the vicinity of magnetically ordered phases, which provides quantitative predictions for ongoing and future experiments aiming at approaching and studying long-range ordered states 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.
More is uncorrelated: Tuning the local correlations of SU(
N) Fermi-Hubbard systems via controlled symmetry breaking
Cold-atom experiments based on alkali-like atoms provide us with a tool to experimentally realize Hubbard models with a large number
N of components. The value of
N can be seen as a new handle to tune the properties of the system, leading to new physics both in the case of fully SU(
N) symmetric systems, or in the presence of controlled symmetry breaking. We focus on the Mott transition at global half filling and we characterize local correlations between particles through the \emph{inter-flavor mutual information}, an experimentally accessible quantity that rigorously measures the distance from the closest gaussian state, unveiling features that cannot be accessed by conventional probes of Mottness. We prove that these correlations are fully independent from local entanglement and quantum discord, and, using Dynamical Mean-Field Theory, we show that the SU(4) system has significantly smaller correlations than the SU(2) counterpart. In the atomic limit we prove that increasing
N further decreases the strength of the correlations. This suggests that a controlled reduction of the symmetry, reducing the number of effective components, can be used to enhance the degree of correlation. We confirm this scenario solving the model for
N=4 and gradually breaking the symmetry via a Raman field, revealing an evolution from the SU(4) to the SU(2) Mott transition as the symmetry-breaking term increases, with a sudden recovery of the large correlations of the SU(2) model at weak Raman coupling in the Mott state. By further exploring the interplay between energy repulsion and the Raman field, we obtain a rich phase diagram with three different phases -- a metal, a band insulator, and a Mott insulator -- all coexisting at a single tricritical point.
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 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.