Entanglement and topological order in cluster states

          @misc{ pirsa_PIRSA:10090098,
            doi = {10.48660/10090098},
            url = {https://pirsa.org/10090098},
            author = {Amico, Luigi},
            keywords = {Quantum Information},
            language = {en},
            title = {Entanglement and topological order in cluster states},
            publisher = {Perimeter Institute},
            year = {2010},
            month = {sep},
            note = {PIRSA:10090098 see, \url{https://pirsa.org}}
          }
          

Abstract

We study a Hamiltonian system describing a three-spin 1/2 cluster like interaction competing with an Ising-like exchange. We show that a cluster state, the ground state of the Hamiltonian in the absence of the Ising term, is provided by a hidden order of topological nature. In the presence of the cluster and Ising couplings, a continuous quantum phase transition occurs in the system, directly connecting a local broken symmetry phase to a cluster phase with the hidden order. At the critical point the Hamiltonian is self-dual. We analyze the geometric entanglement and demonstrate that it can capture the transition, as a single parameter.