Existence of an isolated band in a system of three particles in an optical lattice

We prove the existence of two- and three-particle bound states of the Schrödinger operators and associated to Hamiltonians and of a system of two and three identical bosons on the lattice interacting via pairwise zero-range attractive or repulsive potentials. As a consequence, we show the existence of an isolated band in the two- and three-bosonic systems in an optical lattice.

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