Quantum phase transition between cluster and antiferromagnetic states

TL;DR

This paper investigates a quantum phase transition between cluster and antiferromagnetic states in a spin system, revealing symmetry protected topological order and analyzing entanglement properties, with implications for higher-dimensional systems.

Contribution

It introduces a detailed analysis of the quantum phase transition involving cluster and Ising interactions, highlighting symmetry protected topological order and extending insights to two dimensions.

Findings

Ground state in the cluster phase has symmetry protected topological order.

A continuous quantum phase transition occurs at the critical point.

Indications of a direct transition between antiferromagnetic and valence bond solid states in higher dimensions.

Abstract

We study a Hamiltonian system describing a three spin-1/2 cluster-like interaction competing with an Ising-like exchange. We show that the ground state in the cluster phase possesses symmetry protected topological order. A continuous quantum phase transition occurs as result of the competition between the cluster and Ising terms. At the critical point the Hamiltonian is self-dual. The geometric entanglement is also studied. Our findings in one dimension corroborate the analysis of the two dimensional generalization of the system, indicating, at a mean field level, the presence of a direct transition between an antiferromagnetic and a valence bond solid ground state.