Dimers and cluster integrable systems

Alexander B. Goncharov, Richard Kenyon
2013 Annales Scientifiques de l'Ecole Normale Supérieure  
We show that the dimer model on a bipartite graph Γ on a torus gives rise to a quantum integrable system of special type, which we call a cluster integrable system. The phase space of the classical system contains, as an open dense subset, the moduli space L Γ of line bundles with connections on the graph Γ. The sum of Hamiltonians is essentially the partition function of the dimer model. 5.3 Cluster nature of the resistor network space .
doi:10.24033/asens.2201 fatcat:td6pyut3jjd5taelz6psl2rlqa