Quantum phase transition between cluster and antiferromagnetic states

Abstract

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