Multimer formation in 1D two-component gases and trimer phase in the asymmetric attractive Hubbard model

TL;DR

This paper investigates multimer formation and the trimer phase in asymmetric one-dimensional two-component quantum gases, using theoretical analysis and DMRG simulations to explore phase stability, effects of lattice commensurability, and confinement.

Contribution

It introduces a comprehensive analysis of multimer and trimer phases in asymmetric Hubbard models, highlighting the role of mass asymmetry and total density, supported by numerical phase diagrams.

Findings

Identification of conditions for trimer phase stabilization

Phase diagrams showing the influence of total density

Observation of trimer crystal phase under confinement

Abstract

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.