Quantum phase transition between cluster and antiferromagnetic states

¹ Center for Quantum Technology, National University of Singapore - 117542 Singapore, Singapore
² CNR-MATIS-IMM and Dipartimento di Fisica e Astronomia, Università di Catania C/O ed. 10, viale A. Doria 6, I-95125 Catania, Italy, EU
³ NEST, Scuola Normale Superiore and CNR-INFM - Piazza dei Cavalieri 7, I-56126 Pisa, Italy, EU
⁴ Perimeter Institute for Theoretical Physics - 31 Caroline St. N,Waterloo ON, N2L 2Y5, Canada
⁵ Dipartimento di Fisica and MECENAS, Università di Bari - I-70126 Bari, Italy, EU
⁶ INFN, Sezione di Bari - I-70126 Bari, Italy, EU
⁷ Department of Physics, National University of Singapore - 2 Science Drive 3, 117542 Singapore, Singapore
⁸ Department of Physics, University of Oxford, Clarendon Laboratory - Oxford, OX1 3PU, UK, EU

^a ahamma@perimeterinstitute.ca

Received: 17 February 2011
Accepted: 10 July 2011

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 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.