Luttinger liquid of trimers in the asymmetric Fermi Hubbard model

Ian S. Osborne, Nandini Trivedi, Thereza Paiva

Guillaume Roux, Evgeni Burovski, Th. Jolicœur

We consider two-component one-dimensional quantum gases at special imbalanced commensurabilities which lead to the formation of multimer (multi-particle bound-states) as the dominant order parameter. Luttinger liquid theory supports a mode-locking mechanism in which mass (or velocity) asymmetry is identified as the key ingredient to stabilize such states. While the scenario is valid both in the continuum and on a lattice, the effects of umklapp terms relevant for densities commensurate with the lattice spacing are also mentioned. These ideas are illustrated and confronted with the physics of the asymmetric (mass-imbalanced) fermionic Hubbard model with attractive interactions and densities such that a trimer phase can be stabilized. Phase diagrams are computed using density-matrix renormalization group techniques, showing the important role of the total density in achieving the novel phase. The effective physics of the trimer gas is as well studied. Lastly, the effect of a parabolic confinement and the emergence of a crystal phase of trimers are briefly addressed. This model has connections with the physics of imbalanced two-component fermionic gases and Bose-Fermi mixtures as the latter gives a good phenomenological description of the numerics in the strong-coupling regime.

Maxim Khodas, Michael Pustilnik, A. Kamenev +1 more

V.I. Fernández, A. Iucci, Carlos Naón

Guillaume Roux, Evgeni Burovski, Th. Jolicœur

We consider two-component one-dimensional quantum gases at special imbalanced commensurabilities which lead to the formation of multimer (multiparticle bound-states) as the dominant order parameter. Luttinger liquid theory supports a mode-locking mechanism in which mass (or velocity) asymmetry is identified as the key ingredient to stabilize such states. While the scenario is valid both in the continuum and on a lattice, the effects of umklapp terms relevant for densities commensurate with the lattice spacing are also mentioned. These ideas are illustrated and confronted with the physics of the asymmetric (mass-imbalanced) fermionic Hubbard model with attractive interactions and densities such that a trimer phase can be stabilized. Phase diagrams are computed using density-matrix renormalization group techniques, showing the important role of the total density in achieving the latter phase. The effective physics of the trimer gas is studied as well. Last, the effect of a parabolic confinement and the emergence of a crystal phase of trimers are briefly addressed. This model has connections with the physics of imbalanced two-component fermionic gases and Bose-Fermi mixtures as the latter gives a good phenomenological description of the numerics in the strong-coupling regime.

Giuliano Orso, Evgeni Burovski, Th. Jolicœur

We investigate one dimensional attractive Fermi gases in spin-dependent optical lattices. We show that three-body bound states--"trimers"--exist as soon as the two tunneling rates are different. We calculate the binding energy and the effective mass of a single trimer. We then show numerically that for finite and commensurate densities n(up) = n(down)/2 an energy gap appears, implying that the gas is a one-component Luttinger liquid of trimers with suppressed superfluid correlations. The boundaries of this novel phase are given. We discuss experimental situations to test our predictions.