We pursue three-body bound states in a one-dimensional tight-binding lattice described by the Bose-Hubbard model with strong on-site interaction. Apart from the simple strongly bound ``trimer'' state corresponding to all three particles occupying the same lattice site, we find two novel kinds of weakly bound trimers with energies below and above the continuum of scattering states of a single-particle (``monomer'') and a bound-particle pair (``dimer''). The corresponding binding mechanism can be inferred from an effective Hamiltonian in the strong-coupling regime which contains an exchange interaction between the monomer and the dimer. In the limit of very strong on-site interaction, the exchange-bound trimers attain a universal value of the binding energy. These phenomena can be observed with cold atoms in optical lattices.We pursue three-body bound states in a one-dimensional tight-binding lattice described by the Bose-Hubbard model with strong on-site interaction. Apart from the simple strongly bound ``trimer'' state corresponding to all three particles occupying the same lattice site, we find two novel kinds of weakly bound trimers with energies below and above the continuum of scattering states of a single-particle (``monomer'') and a bound-particle pair (``dimer''). The corresponding binding mechanism can be inferred from an effective Hamiltonian in the strong-coupling regime which contains an exchange interaction between the monomer and the dimer. In the limit of very strong on-site interaction, the exchange-bound trimers attain a universal value of the binding energy. These phenomena can be observed with cold atoms in optical lattices.

arXiv:0907.3111Physical Review AJan 4, 201051 citations

Few-Body Bound States on a Three-Dimensional and Two-Dimensional Lattice and Continuum Limit for One-Dimensional Many-Body System.

S. Rudin

Jan 1, 19840 citations

Few body bound states in a lattice

Jugal Talukdar, D. Blume

Bulletin of the American Physical SocietyMay 31, 20180 citations

Effective mass of three-body complexes for finite-range potentials on a lattice

S. Rudin

For the bound state of three identical lattice bosons interacting via attractive potentials (with strength U, range r, and repulsive core ${U}_{0}$ ) we investigate how its mass depends on U for large U. We find that the mobility of this bound complex depends strongly on r and that for a nearest-neighbor interaction (r=1) it may depend strongly on ${U}_{0}$ .For the bound state of three identical lattice bosons interacting via attractive potentials (with strength U, range r, and repulsive core ${U}_{0}$) we investigate how its mass depends on U for large U. We find that the mobility of this bound complex depends strongly on r and that for a nearest-neighbor interaction (r=1) it may depend strongly on ${U}_{0}$.

Physical Review AFeb 1, 19866 citations

Three-Body Bound States on a Lattice

Daniel Charles Mattis, Sergey Rudin

The theory of three-body bound states for particles moving on a lattice and interacting with attractive two-body pointlike potentials is presented. The applications are to bosons, fermions (no three-body bound states are found), and magnons. When a three-body bound state forms in three dimensions, it does so discontinuously. Thus there is a maximum size for the three-body bound state, of approximately two lattice constants. Some of the various analyses are relevant to magnetism and superconductivity.The theory of three-body bound states for particles moving on a lattice and interacting with attractive two-body pointlike potentials is presented. The applications are to bosons, fermions (no three-body bound states are found), and magnons. When a three-body bound state forms in three dimensions, it does so discontinuously. Thus there is a maximum size for the three-body bound state, of approximately two lattice constants. Some of the various analyses are relevant to magnetism and superconductivity.

Physical Review LettersFeb 27, 198421 citations

For the bound state of three identical lattice bosons interacting via attractive potentials (with strength U, range r, and repulsive core

{U}_{0}

) we investigate how its mass depends on U for large U. We find that the mobility of this bound complex depends strongly on r and that for a nearest-neighbor interaction (r=1) it may depend strongly on

{U}_{0}