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arXiv:1012.4499 · New Journal of Physics

Magnetism and domain formation in SU(3)-symmetric multi-species Fermi mixtures

Irakli Titvinidze, A Privitera, S-Y Chang, Sebastian Diehl, M A Baranov, Andrew J. Daley, Walter Hofstetter

Published Mar 16, 2011• 37 citations
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Abstract

We study the phase diagram of an SU(3)-symmetric mixture of three-component ultracold fermions with attractive interactions in an optical lattice, including the additional effect on the mixture of an effective three-body constraint induced by three-body losses. We address the properties of the system in D ⩾2 by using dynamical mean-field theory and variational Monte Carlo techniques. The phase diagram of the model shows a strong interplay between magnetism and superfluidity. In the absence of the three-body constraint (no losses), the system undergoes a phase transition from a color superfluid (c-SF) phase to a trionic phase, which shows additional particle density modulations at half-filling. Away from the particle–hole symmetric point the c-SF phase is always spontaneously magnetized, leading to the formation of different c-SF domains in systems where the total number of particles of each species is conserved. This can be seen as the SU(3) symmetric realization of a more general tendency for phase separation in three-component Fermi mixtures. The three-body constraint strongly disfavors the trionic phase, stabilizing a (fully magnetized) c-SF also at strong coupling. With increasing temperature we observe a transition to a non-magnetized SU(3) Fermi liquid phase.

DOI
10.1088/1367-2630/13/3/035013

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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.
We investigate three-component (colors) fermionic atoms with anisotropic attractive interactions in optical lattices at half filling using the dynamical mean field theory. In the weakly interacting region the color superfluid (CSF) state emerges, where atoms with two of three colors form the Cooper pairs. As the interaction is increased, a first-order quantum phase transition to the trionic state occurs, where singlet bound states of three different color atoms are formed. We show that the trionic state survives up to a fairly large anisotropic region. The phase diagram for the CSF and trionic states is obtained.
We investigate the finite-temperature properties of attractive three-component (colors) fermionic atoms in optical lattices using a self-energy functional approach. As the strength of the attractive interaction increases in the low-temperature region, we observe a second-order transition from a Fermi liquid to a color superfluid (CSF), where atoms from two of the three colors form Cooper pairs. In the strong attractive region, we observe a first-order transition from a CSF to a trionic state, where three atoms with different colors form singlet bound states. A crossover between a Fermi liquid and a trionic state is observed in the high-temperature region. We present a phase diagram covering zero to finite temperatures. We demonstrate that the CSF transition temperature is enhanced by the anisotropy of the attractive interaction.
In optical lattices attractive ultracold fermions with three hyperfine-spin components (colors) can form three fermionic configurations depending on the interactions---unbound fermions, on-site trions, and off-site trions---leading to the coexistence of multiple fermionic species in the ordered phase, which demonstrates that the attractive three-color fermions are unique from other correlated fermion systems and may host intriguing phases and phase transitions. At temperatures below the superexchange energy scale, we employ the determinant quantum Monte Carlo (QMC) method to investigate the phases and phase transitions in the half-filled attractive three-color Hubbard model on a honeycomb lattice where the Hubbard interactions are color dependent (anisotropic interactions) and the coupling between color 3 and colors (1, 2) serves as a control parameter. In the coupling regime where on-site and off-site trions coexist, our QMC simulations demonstrate coexisting N\'eel and charge density wave (CDW) orders which are common in condensed matter but rare in ultracold atoms. At weak coupling where the color superfluid (CSF) order is scattered by color-3 fermions, we find that very small coupling of color 3 with colors (1, 2) can destroy the CSF order and that the vanishing of the CSF order is not immediately accompanied by the emergence of the on-site trionic phase, which strikingly disagrees with the prevalent results of dynamical mean-field theory. The underlying mechanisms of the coexisting N\'eel/CDW orders and of the CSF order breaking are also presented based on intuitive physical pictures.