Global-to-local incompatibility, monogamy of entanglement, and ground-state dimerization: Theory and observability of quantum frustration in systems with competing interactions

S. M. Giampaolo, B. C. Hiesmayr, and F. Illuminati
Phys. Rev. B 92, 144406 – Published 6 October 2015

Abstract

Frustration in quantum many-body systems is quantified by the degree of incompatibility between the local and global orders associated, respectively, with the ground states of the local interaction terms and the global ground state of the total many-body Hamiltonian. This universal measure is bounded from below by the ground-state bipartite block entanglement. For many-body Hamiltonians that are sums of two-body interaction terms, a further inequality relates quantum frustration to the pairwise entanglement between the constituents of the local interaction terms. This additional bound is a consequence of the limits imposed by monogamy on entanglement shareability. We investigate the behavior of local pair frustration in quantum spin models with competing interactions on different length scales and show that valence bond solids associated with exact ground state dimerization correspond to a transition from generic frustration, i.e., geometric, common to classical and quantum systems alike, to genuine quantum frustration, i.e., solely due to the noncommutativity of the different local interaction terms. We discuss how such frustration transitions separating genuinely quantum orders from classical-like ones are detected by observable quantities such as the static structure factor and the interferometric visibility.

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  • Received 19 January 2015
  • Revised 19 September 2015

DOI:https://doi.org/10.1103/PhysRevB.92.144406

©2015 American Physical Society

Authors & Affiliations

S. M. Giampaolo1,2, B. C. Hiesmayr2, and F. Illuminati1,3,4,*

  • 1Dipartimento di Ingegneria Industriale, Università degli Studi di Salerno, Via Giovanni Paolo II 132, I-84084 Fisciano (SA), Italy
  • 2University of Vienna, Faculty of Physics, Boltzmanngasse 5, 1090 Vienna, Austria
  • 3CNISM Unità di Salerno, I-84084 Fisciano (SA), Italy
  • 4INFN, Sezione di Napoli, Gruppo collegato di Salerno, I-84084 Fisciano (SA), Italy

  • *Corresponding author: fabrizio.illuminati@gmail.com

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Issue

Vol. 92, Iss. 14 — 1 October 2015

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