Solving the quantum dimer and six vertex models one electric field line at a time

Understand

The nature and the very existence of the resonant plaquette valence bond state that separates the classical columnar phase and the Rokhsar and Kivelson point in the quantum dimer model remains unsettled.

• Here we take a different line of attack on this model, and on the closely related six vertex model, by exploiting the global conservation law of the number of electric field lines.
• This allows us to study a single fluctuating electric field line which we show maps exactly onto a one dimensional spin chain.
• In the case of the six vertex model, the electric field line maps onto the celebrated spin 1/2 XXZ model which can be solved exactly.