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arXiv:2111.10316 · Physical review. B./Physical review. B

Kinetic formation of trimers and multimers in a spinless fermionic chain

Lorenzo Gotta, Leonardo Mazza, Pascal Simon, Guillaume Roux

Published Apr 19, 2022• 5 citations
arXivHTMLPDF

Abstract

We study a chain of spinless fermions with a multimer hopping term which kinematically favors the formation of multimers and competes with single-particle hopping. We argue that this model generically stabilizes two different multimer phases, as well as intermediate phases where the free-fermion and multimer fluids coexist and do not spatially separate. Using density-matrix renormalization group techniques, we establish the phase diagram of the model in the case of trimers. For one of the intermediate phases, hybridization between the fermions and trimers liquids does occur and the onset of their correlations is well captured by a generalized BCS-like ansatz. The case of tetramers is finally addressed.

DOI
10.1103/physrevb.105.134512

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We study a chain of spinless fermions with a multimer hopping term which kinematically favors the formation of multimers and competes with single-particle hopping. We argue that this model generically stabilizes two different multimer phases, as well as intermediate phases where the free-fermion and multimer fluids coexist and do not spatially separate. Using density-matrix renormalization group techniques, we establish the phase diagram of the model in the case of trimers. For one of the intermediate phases, hybridization between the fermions and trimers liquids does occur and the onset of their correlations is well captured by a generalized BCS-like ansatz. The case of tetramers is finally addressed.
We compute the phase diagram of a one-dimensional model of spinless fermions with pair hopping and nearest-neighbor interaction, first introduced by Ruhman and Altman, using the density-matrix renormalization group combined with various analytical approaches. Although the main phases are a Luttinger liquid of fermions and a Luttinger liquid of pairs, we also find remarkable phases in which only a fraction of the fermions are paired. In such a case, two situations arise: either fermions and pairs coexist spatially in a two-fluid mixture, or they are spatially segregated leading to phase separation. These results are supported by several analytical models that describe in an accurate way various relevant cuts of the phase diagram. Last, we identify relevant microscopic observables that capture the presence of these two fluids: while originally introduced in a phenomenological way, they support a wider application of two-fluid models for describing pairing phenomena.
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.
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.
The linear renormalization-group transformation is used to study the thermodynamics of weakly coupled spinless fermion chains at half-filling. The model consists of a competing nearest-neighbour Coulomb repulsion and kinetic energy terms. The specific heat and the nearest-neighbour correlation function are studied as functions of temperature by varying the ratio of Coulomb repulsion to kinetic energy. The role of an interchain hopping is studied and the metal–insulator phase transition temperature as a function of hopping parameters is discussed.
The Hubbard and spinless fermion chains are paradigms of strongly correlated systems, very well understood using the Bethe ansatz, density matrix renormalization group (DMRG), and field theory/renormalization group (RG) methods. They have been applied to one-dimensional materials and have provided important insights for understanding higher-dimensional cases. Recently, an interacting fermion model has been introduced, with possible applications to topological materials. It has a single Majorana fermion operator on each lattice site and interactions with the shortest possible range that involve four sites. We present a thorough analysis of the phase diagram of this model in one dimension using field-theory/RG and DMRG methods. It includes a gapped supersymmetric region and a gapless phase with coexisting Luttinger liquid and Ising degrees of freedom. In addition to a first-order transition, three critical points occur: tricritical Ising, Lifshitz, and a generalization of the commensurate-incommensurate transition. We also survey various gapped phases of the system that arise when the translation symmetry is broken by dimerization and find both trivial and topological phases with 0, 1, and 2 Majorana zero modes bound to the edges of the chain with open boundary conditions.