# Roksar-Kivelson Hamiltonian for a Quantum Dimer Gas

1. May 12, 2014

### Shinn497

2. May 12, 2014

### Hypersphere

I'm not familiar with this particular model, so I don't know the connection with the fractional quantum Hall effect or the eigenstates. However, it seems quite clear to me that while the spins themselves are at fixed positions, the dimerized bonds are free to move (as in changing which spins are dimerized). This gives you a notion of kinetic energy (terms proportional to t), while if the dimers do not move, there is an associated potential energy (terms proportional to v).

Based on your second question at SE, I'm not sure if you see why I picked out those particular terms as kinetic/potential. This should be clear if you evaluate the four matrix elements of the Hamiltonian, or just noticing that there are two projection operators (which cannot change the state, i.e. cannot move dimers) and two operators always leading to a transition. (I'd spell it out more, but I'm not sure how to typeset it on the forum.)