Classical and quantum dimers on the star lattice

Understand

We consider dimers on the star lattice (aka the 3-12, Fisher, expanded kagome or triangle-honeycomb lattice).

• We show that dimer coverings on this lattice have Z_2 arrow and pseudo-spin representations analogous to those for the kagome lattice, and use these to construct an exactly solvable quantum dimer model (QDM) with a Rokhsar-Kivelson (RK) ground state.
• This QDM, first discussed by Moessner and Sondhi from a different point of view, is the star-lattice analogue of a kagome-lattice QDM analyzed by Misguich et al.
• We give a detailed analysis of various properties of the classical equal-weight dimer model on the star lattice, most of which are related to those of the RK state.