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arXiv:1002.3685 · Physical Review A

Color-charge separation in trapped SU( 3 ) fermionic atoms

Tobias Ulbricht, Rafael A. Molina, Ronny Thomale, Peter Schmitteckert

Published Jul 7, 2010• 14 citations
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Abstract

Cold fermionic atoms with three different hyperfine states with SU($3$) symmetry confined in one-dimensional optical lattices show color-charge separation, generalizing the conventional spin-charge separation for interacting SU($2$) fermions in one dimension. Through time-dependent density-matrix renormalization-group simulations, we explore the features of this phenomenon for a generalized SU($3$) Hubbard Hamiltonian. In our numerical simulations of finite-size systems, we observe different velocities of the charge and color degrees of freedom when a Gaussian wave packet or a charge (color) density response to a local perturbation is evolved. The differences between attractive and repulsive interactions are explored and we note that neither a small anisotropy of the interaction, breaking the SU($3$) symmetry, nor the filling impedes the basic observation of these effects.

DOI
10.1103/physreva.82.011603

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One of the key features of one-dimensional systems is the phenomenon of spin–charge separation. We show this separation of spin and charge in real time in the 1D Hubbard model by the application of the adaptive time-dependent density-matrix renormalization group method. It is found for single particle excitations and density wave packets far beyond the low-energy Luttinger liquid theory. An experimental set-up is proposed on how to observe the spin–charge separation with ultracold Fermi gases in a harmonic trap using the presence of the Mott-insulator region. Quantitative estimates for experimental parameters are given.
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.
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In recent years, ultracold bosonic and fermionic atom gases in optical lattices have allowed us to realize experimentally phenomena originally predicted or observed in condensed matter physics with unprecedented control and purity. Among others, proposals have been made to demonstrate a key feature of one dimensional (1D) quantum systems, the so-called spin-charge separation, which has been quite elusive in condensed matter systems. However, as we want to discuss in this paper using the time-dependent density-matrix renormalization group (DMRG), beyond a mere demonstration of spin-charge separation cold atom gases will also shed light on previously inaccessible aspects of this phenomenon. Moreover, the previous proposals for experimental realizations will be revisited taking into account the modelling of an external magnetic field.
Cold fermionic atoms with three different hyperfine states confined in optical lattices show pronounced atomic density waves (ADWs). These ADWs are pinned due to the confining potential that traps the atoms in the optical lattice and can be considered a crystal phase of strongly bound trions (CPT). We show that the crystalline phase is incompressible and robust against anisotropic interactions. We also show that it is generic in the presence of the trap due to its incompressibility. Numeric density matrix renormalization group calculations show evidence of a crossover between a trionic superfluid and the CPT state as a function of the strength of the interaction and as a function of the anisotropy of the interaction.
We investigate three-component (colors) repulsive fermionic atoms in optical lattices using the dynamical mean-field theory. Depending on the anisotropy of the repulsive interactions, either a color density-wave state or a color-selective staggered state appears at half filling. In the former state, pairs of atoms with two of the three colors and atoms with the third color occupy different sites alternately. In the latter state, atoms with two of the three colors occupy different sites alternately and atoms with the third color are itinerant throughout the system. When the interactions are isotropic, both states are degenerate. We discuss the results using an effective model.