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

TL;DR

This paper introduces an exactly solvable family of many-body models with cluster and Ising interactions, revealing distinct nematic and topological phases, and analyzing their entanglement properties.

Contribution

It provides an analytical solution for a family of models exhibiting novel phases and entanglement features, serving as a prototype for studying complex spin orderings.

Findings

Critical point independent of cluster size

Cluster phase is nematic for even n

No bipartite or (n+1)-partite entanglement

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 multi-particle 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 non-trivial 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 analytically solvableness the $n$-cluster-Ising models serve as a prototype for studying non trivial-spin orderings and due to their peculiar entanglement properties they serve as a potential reference system for the performance of quantum information tasks.