Exactly solvable interacting vertex models

TL;DR

This paper introduces a new family of exactly solvable interacting vertex models that extend the six-vertex model with additional long-range interactions, and demonstrates their integrability through a matrix product ansatz.

Contribution

It presents a novel integrable vertex model with extended interactions and provides a solution method using a matrix product ansatz, linking it to generalized quantum spin chains.

Findings

Models are exactly solvable using matrix product ansatz.

Transfer matrices generate commuting conserved charges.

Identifies integrable generalizations of the XXZ chain with hard-core interactions.

Abstract

We introduce and solvev a special family of integrable interacting vertex models that generalizes the well known six-vertex model. In addition to the usual nearest-neighbor interactions among the vertices, there exist extra hard-core interactions among pair of vertices at larger distances.The associated row-to-row transfer matrices are diagonalized by using the recently introduced matrix product {\it ansatz}. Similarly as the relation of the six-vertex model with the XXZ quantum chain, the row-to-row transfer matrices of these new models are also the generating functions of an infinite set of commuting conserved charges. Among these charges we identify the integrable generalization of the XXZ chain that contains hard-core exclusion interactions among the spins. These quantum chains already appeared in the literature. The present paper explains their integrability.