Quantum phase transition between cluster and antiferromagnetic states

• Published in: Europhysics letters Vol. 95; no. 5; p. 50001
• Main Authors: Son, W., Amico, L., Fazio, R., Hamma, A., Pascazio, S., Vedral, V.
• Format: Journal Article
• Language: English
• Published: EPS, SIF, EDP Sciences and IOP Publishing 01-09-2011
• Subjects: 03.65.Ta; 03.65.Ud; 03.67.-a
• ISSN: 0295-5075; 1286-4854
• DOI: 10.1209/0295-5075/95/50001

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 and used to investigate the quantum phase transition. 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.