Topological and nematic ordered phases in many-body cluster-Ising models

Author(s)
S. M. Giampaolo, B. C. Hiesmayr
Abstract

We present a fully analytically solvable family of models with many-body cluster interaction and Ising interaction. This family exhibits two phases, dubbed cluster and Ising phases, respectively. The critical point turns out to be independent of the cluster size n + 2 and is reached exactly when both interactions are equally weighted. For even n we prove that the cluster phase corresponds to a nematic ordered phase and in the case of odd n to a symmetry-protected topological ordered phase. Though complex, we are able to quantify the multiparticle entanglement content of neighboring spins. We prove that there exists no bipartite or, in more detail, no n + 1-partite entanglement. This is possible since the nontrivial symmetries of the Hamiltonian restrict the state space. Indeed, only if the Ising interaction is strong enough ( local) genuine n + 2-partite entanglement is built up. Due to their analytical solvableness the n-cluster-Ising models serve as a prototype for studying nontrivial-spin orderings, and due to their peculiar entanglement properties they serve as a potential reference system for the performance of quantum information tasks.

Organisation(s)
Particle Physics
External organisation(s)
Theory@Elettra Group, CNR.INFM DEMOCRITOS, National Simulation Center
Journal
Physical Review A
Volume
92
No. of pages
9
ISSN
1050-2947
DOI
https://doi.org/10.1103/PhysRevA.92.012306
Publication date
07-2015
Peer reviewed
Yes
Austrian Fields of Science 2012
103025 Quantum mechanics, 103034 Particle physics
Keywords
Portal url
https://ucris.univie.ac.at/portal/en/publications/topological-and-nematic-ordered-phases-in-manybody-clusterising-models(d78ae382-ed54-45c5-be38-5bf4022929f9).html