Towards Yang-Baxter integrability of quantum crystal melting: From Kagome lattice to vertex models

Abstract

This paper considers aspects of a Kagome lattice system with states classified by plane partitions. Using two sets of free fermions, we rewrite the lattice in terms of two families of spin chains. In this formalism, the quantum crystals Hamiltonian becomes more transparent, and we determine expressions for the first 3 levels of plane partition states. A classical statistical model associated to local configurations in the Kagome lattice is also defined, and we show that a reduction of this classical system gives two Yang-Baxter integrable subsystems analogous to a descendant of the 6-vertex model.