Exact solutions of a class of S=1 quantum Ising spin models

TL;DR

This paper introduces an exact solution method for a class of spin-1 quantum Ising models using a hole decomposition scheme, enabling precise calculation of thermodynamic properties and phase diagrams.

Contribution

It presents a novel hole decomposition approach that maps spin-1 models onto S=1/2 transverse Ising models, simplifying analysis and enabling exact solutions.

Findings

Exact solutions for thermodynamic quantities derived

Ground state phase diagrams mapped for uniform and dimerized chains

Thermodynamic properties discussed in detail

Abstract

We propose a hole decomposition scheme to exactly solve a class of spin-1 quantum Ising models with transverse or longitudinal single-ion anisotropy. In this scheme, the spin-1 model is mapped onto a family of the $S=1/2$ transverse Ising models, characterized by the total number of holes. A recursion formula is derived for the partition function based on the reduced $S=1/2$ Ising model. This simplifies greatly the summation over all the hole configurations. It allows the thermodynamic quantities to be rigorously determined in the thermodynamic limit. The ground state phase diagram is determined for both the uniform and dimerized spin chains. The corresponding thermodynamic properties are calculated and discussed.