Correlation functions in one-dimensional spin lattices with Ising and Heisenberg bonds

TL;DR

This paper introduces a general exact method for calculating correlation functions in one-dimensional spin models with mixed Ising and quantum spins, applicable to chains with small quantum clusters, and demonstrates it on specific chain types.

Contribution

It develops a new general technique for exact correlation function calculations in mixed Ising-Heisenberg spin chains, extending previous classical transfer matrix methods.

Findings

Correlation functions decay governed by a single correlation length.

Explicit expressions for matrix operators in the technique.

Application to symmetric diamond and asymmetric sawtooth chains.

Abstract

A general technique of exact calculation of any correlation functions for the special class of one-dimensional spin models containing small clusters of quantum spins assembled to a chain by alternating with the single Ising spins is proposed. The technique is a natural generalization of that in the models solved by a classical transfer matrix. The general expressions for corresponding matrix operators which are the key components of the technique are obtained. As it is clear from the general principles, the decay of the correlation functions of various types is explicitly shown to be governed by a single correlation length. The technique is illustrated by two examples: symmetric diamond chain and asymmetric sawtooth chain.