Exact solution of quasi two and three dimensional quantum spin models

TL;DR

This paper introduces a class of quasi two- and three-dimensional quantum spin models with exact solutions, constructed via twisting transformations, expanding the set of integrable quantum lattice models.

Contribution

It presents a novel construction of quasi 2D and 3D quantum spin models with exact solutions using twisting transformations and symmetry properties.

Findings

Models are quantum integrable with explicit R-matrix solutions

Eigenvalue problems are exactly solvable due to model symmetries

The approach extends integrability to more complex lattice geometries

Abstract

A class of quasi two and three dimensional quantum lattice spin models with nearest and next nearest neighbour interactions is proposed. The basic idea of construction is to introduce interactions in an array of XXZ spin chains through twisting transformation. The models belong to quantum integrable systems allowing explicit R-matrix solution. The eigenvalue problem can be solved exactly using some symmetry of the models.