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arXiv · 2410.07070

A two-boson lattice Hamiltonian with interactions up to next-neighboring sites

S. N. Lakaev·A. K. Motovilov·M. O. Akhmadova
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Abstract

A system of two identical spinless bosons on the two-dimensional lattice is considered under the assumption that on-site and first and second nearest-neighboring site interactions between the bosons are only nontrivial and that these interactions are of magnitudes $\gamma$, $\lambda$, and $\mu$, respectively. A partition of the $(\gamma,\lambda,\mu)$-space into connected components is established such that, in each connected component, the two-boson Schroedinger operator corresponding to the zero quasi-momentum of the center of mass has a definite (fixed) number of eigenvalues, which are situated below the bottom of the essential (continuous) spectrum and above its top. Moreover, for each connected component, a sharp lower bound is established on the number of isolated eigenvalues for the two-boson Schr\"odinger operator corresponding to any admissible nonzero value of the center-of-mass quasimomentum.

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S. N. Lakaev, A. K. Motovilov, M. O. Akhmadova. 2024-10-09. A two-boson lattice Hamiltonian with interactions up to next-neighboring sites. https://arxiv.org/abs/2410.07070

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