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

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.

arXiv comment10 pages, 9 figures

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• Genuine Multipartite Entanglement in the $3$-Photon Decay of Positronium
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• The Frustration of being Odd: How Boundary Conditions can destroy Local Order
• Mutual information and spontaneous symmetry breaking
• Effects of defects in the XY chain with frustrated boundary conditions
• n-cluster models in a transverse magnetic field
• Resilience of the topological phases to frustration
• Topological Frustration can modify the nature of a Quantum Phase Transition
• String order via Floquet interactions in atomic systems
• Towards a phase diagram of the topologically frustrated XY chain
• Random unitaries, Robustness, and Complexity of Entanglement
• Multipartite entanglement and quantum error identification in $D$-dimensional cluster states
• The global phase diagram of the cluster-XY spin chain with dissipation
• Hierarchy of emergent cluster states by measurement from symmetry-protected-topological states with large symmetry to subsystem cat state
• The Interplay between Frustration and Entanglement in Many-Body Systems
• Long-distance genuine multipartite Entanglement between Magnetic Defects in Spin Chains
• Quench of symmetry broken ground states
• Emergent gapless spiral phases and conformal Lifshitz criticality in the cluster Ising model with off-diagonal interactions
• The fate of local order in topologically frustrated spin chains
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• Quantum cluster kink and ring frustration
• Emergence of long-range entanglement and odd-even effect in periodic generalized quantum cluster models