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

TL;DR

This paper explores the integrability of quantum crystal melting on Kagome lattices by reformulating the system with free fermions, revealing connections to Yang-Baxter integrable vertex models and providing explicit state level expressions.

Contribution

It introduces a novel fermionic formalism for Kagome lattice systems and identifies Yang-Baxter integrable subsystems related to classical vertex models.

Findings

Explicit expressions for the first three levels of plane partition states.

Identification of two Yang-Baxter integrable subsystems.

Reduction of the classical model to known 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 with 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.