Cluster-Based Haldane States in Spin-1/2 Cluster Chains

TL;DR

This paper proposes a novel method to realize Haldane states using chains of half-spin clusters, facilitating experimental realization and quantum computation applications.

Contribution

It introduces a new approach to generate Haldane states from half-spin systems by using cluster chains, including a concrete procedure for odd-spin clusters.

Findings

Ground state of two-spin clusters corresponds to AKLT state.

A procedure to induce Haldane state in odd-spin clusters.

Illustration with a 5-spin cluster chain.

Abstract

The Haldane state is a typical quantum and topological state of matter, which exhibits an edge state corresponding to symmetry-protected topological order in a one-dimensional integer spin chain. This edge state can be utilized for a processing unit of quantum computation. Its realization, however, has difficulties with synthesis of integer spin compounds. In contrast, one-half spin systems are more designable due to recent progress on intended synthesis of organic materials, quantum dots, and optical lattices. Here we propose a concept to design the Haldane state with one-half spins by making use of a chain composed of one-half spin clusters. If the clusters contains two spins, the ground state of a chain corresponds to the Affleck--Kennedy--Lieb--Tasaki state. In the case of an odd number of spins in the clusters, we propose a concrete procedure to construct a field-induced Haldane state. We illustrate the procedure with a 5-spin cluster chain.