Bose-Hubbard Hamiltonian from generalized commutation rules

TL;DR

This paper derives the Bose-Hubbard Hamiltonian with on-site interactions from a free Hamiltonian using generalized commutation relations, linking concepts from high energy physics to condensed matter models.

Contribution

It introduces a novel approach to obtain the Bose-Hubbard Hamiltonian via generalized commutation relations, bridging high energy physics and condensed matter.

Findings

Spectrum can be formally derived using algebraic properties of generalized operators.

First application of generalized commutation relations in this context.

Provides a new algebraic framework for analyzing Bose-Hubbard systems.

Abstract

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.