Bose-Hubbard Hamiltonian from generalized commutation rules

In a first order approximation, the Bose-Hubbard Hamiltonian with on site interaction is obtained from the free Hamiltonian (U=0) and generalized commutation relation for the annihilation-creation operators. Similar generalized commutation relations were used for the first time in high energy physics. The spectrum of the system can be found formally by using the algebraic properties of the generalized operators.