Stability of (N+1) -body fermion clusters in a multiband Hubbard model

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Iskin M., KELEŞ A.

Physical Review A, vol.106, no.3, 2022 (SCI-Expanded) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 106 Issue: 3
  • Publication Date: 2022
  • Doi Number: 10.1103/physreva.106.033304
  • Journal Name: Physical Review A
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Chemical Abstracts Core, Compendex, INSPEC, zbMATH, DIALNET
  • Middle East Technical University Affiliated: Yes


© 2022 American Physical Society. We start with a variational approach and derive a set of coupled integral equations for the bound states of N identical spin-↑ fermions and a single spin-↓ fermion in a generic multiband Hubbard Hamiltonian with an attractive on-site interaction. As an illustration, we apply our integral equations to the one-dimensional sawtooth lattice up to N≤3, i.e., to the (3+1)-body problem, and we reveal not only the presence of tetramer states in this two-band model but also their quasiflat dispersion when formed in a flat band. Furthermore, for N={4,5, »,10}, our density-matrix renormalization-group simulations and exact diagonalization suggest the presence of larger and larger multimers with lower and lower binding energies, conceivably without an upper bound on N. These peculiar (N+1)-body clusters are in sharp contrast with the exact results on the single-band linear-chain model where none of the N≥2 multimers appear. Hence their presence must be taken into account for a proper description of the many-body phenomena in flat-band systems, e.g., they may suppress superconductivity especially when there exists a large spin imbalance.