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

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 as two families of spin chains. In this formalism, the quantum crystals Hamiltonian becomes more transparent, and we explicitly present the first 3 levels of plane partition states. A classical statistical model is also defined in terms of the Kagome lattice local configurations, and we show that it gives origin to two Yang-Baxter integrable subsystems related to a descendant of the 6-vertex model.