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

We start with a variational approach and derive a set of coupled integral equations for the bound states of N identical spin-up arrow fermions and a single spin-down arrow 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.