Bose-Hubbard models with on-site and nearest-neighbor interactions: Exactly solvable case

Saidakhmat Lakaev, Shokhrukh Kholmatov, Shakhobiddin Khamidov

We study the discrete spectrum of the two-particle Schrödinger operator ${\hat{H}}_{\mu \lambda }(K),$ $K\in {\mathbb{T}}^2,$ associated to the Bose-Hubbard Hamiltonian ${\hat{\mathbb{H}}}_{\mu \lambda }$ of…