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# Critical entropies and magnetic-phase-diagram analysis of ultracold three-component fermionic mixtures in optical lattices

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### Abstract

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.

### Most cited references2

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### Observation of antiferromagnetic correlations in the Hubbard model with ultracold atoms

(2014)
Ultracold atoms in optical lattices have great potential to contribute to a better understanding of some of the most important issues in many-body physics, such as high-$$T_c$$ superconductivity. The Hubbard model describes many of the features shared by the copper oxides, including an interaction-driven Mott insulating state and an antiferromagnetic (AFM) state. Optical lattices filled with a two-spin-component Fermi gas of ultracold atoms can faithfully realise the Hubbard model with readily tunable parameters, and thus provide a platform for the systematic exploration of its phase diagram. Realisation of strongly correlated phases, however, has been hindered by the need to cool the atoms to temperatures as low as the magnetic exchange energy, and also by the lack of reliable thermometry. Here we demonstrate spin-sensitive Bragg scattering of light to measure AFM spin correlations in a realisation of the 3D Hubbard model at temperatures down to 1.4 times that of the AFM phase transition. This temperature regime is beyond the range of validity of a simple high-temperature series expansion, which brings our experiment close to the limit of the capabilities of current numerical techniques. We reach these low temperatures using a unique compensated optical lattice technique, in which the confinement of each lattice beam is compensated by a blue-detuned laser beam. The temperature of the atoms in the lattice is deduced by comparing the light scattering to determinantal quantum Monte Carlo and numerical linked-cluster expansion calculations. Further refinement of the compensated lattice may produce even lower temperatures which, along with light scattering thermometry, would open avenues for achieving and characterising other novel quantum states of matter, such as the pseudogap regime of the 2D Hubbard model.
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### Giant spin oscillations in an ultracold Fermi sea

(2013)
Collective behavior in many-body systems is the origin of many fascinating phenomena in nature ranging from swarms of birds and modeling of human behavior to fundamental magnetic properties of solids. We report on the first observation of collective spin dynamics in an ultracold Fermi sea with large spin: We observe long-lived and large-amplitude coherent spin oscillations, driven by local spin interactions. At ultralow temperatures, Pauli blocking stabilizes the collective behavior and the Fermi sea behaves as a single entity in spin space. With increasing temperature, we observe a stronger damping associated with particle-hole excitations. As a striking feature, we find a high-density regime where excited spin configurations are collisionally stabilized.
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### Author and article information

###### Journal
2015-06-25
2015-08-25
1506.07642
10.1103/PhysRevA.92.023633

Phys. Rev. A 92, 023633 (2015)
8 pages, 5 figures
cond-mat.quant-gas cond-mat.str-el

Condensed matter, Quantum gases & Cold atoms