n-cluster models in a transverse magnetic field

Abstract

In this paper we analize a family of one dimensional fully analytically solvable models, named the n-cluster models in a transverse magnetic field, in which a many-body cluster interaction competes with a uniform transverse magnetic field. These models, independently by the cluster size n + 2, exibit a quantum phase transition, that separates a paramagnetic phase from a cluster one, that corresponds to a nematic ordered phase or a symmetry-protected topological ordered phase for even or odd n respectively. Due to the symmetries of the spin correlation functions, we prove that these models have no genuine n+2-partite entanglement. On the contrary, a non vanishing concurrence arises between spins at the endpoints of the cluster, for a magnetic field strong enough. Due to their analyticity and peculiar entanglement properties, the n-cluster models in a transverse magnetic field serve as a prototype for studying non trivial-spin orderings and as a potential reference system for the applications of quantum information tasks.

8 pages, 7 figures

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• Resilience of the topological phases to frustration
• Topological Frustration can modify the nature of a Quantum Phase Transition
• Efficient ground state preparation in variational quantum eigensolver with symmetry-breaking layers
• The fate of local order in topologically frustrated spin chains
• Numerically efficient unitary evolution for Hamiltonians beyond nearest-neighbors
• Emergence of long-range entanglement and odd-even effect in periodic generalized quantum cluster models
• Quantum cluster kink and ring frustration