Take the 2-minute tour ×
Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It's 100% free, no registration required.

$H = -\sum\limits_{i,j} A_{ij} c_i^{\dagger} c_j + \frac{U}{2} \sum\limits_i(c_i^\dagger c_i)(c_i^\dagger c_i -1)$ is defined to be a Hamiltonian for modeling quantum random walk of identical particles on a graph (Hubbard Model). A particle can make transition from one vertex to another if there is an edge between then and a double-occupancy charge $U$ is imposed. $A$ is the adjacency matrix of the finite graph.

I vaguely understand that first term is about transition from vertex j to i ( destroyed at j and created at i ) and second term will result in $U$ when acted on state where two particle occupy same state. How do I make this understanding rigorous and obtain the matrix elements of $H$ when there are two bosonic particles in some vertices initially. What corresponds to energy, and eigenfunction of the $H$?

share|improve this question
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.