Global-to-local incompatibility, monogamy of entanglement, and ground-state dimerization

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

Organisation(s)
Particle Physics
External organisation(s)
Università degli Studi di Salerno, CNISM, Unita Salerno, Istituto Nazionale di Fisica Nucleare (INFN), Roma
Journal
Physical Review B
Volume
92
No. of pages
11
ISSN
1098-0121
DOI
https://doi.org/10.1103/PhysRevB.92.144406
Publication date
10-2015
Peer reviewed
Yes
Austrian Fields of Science 2012
103019 Mathematical physics, 103025 Quantum mechanics
Keywords
Portal url
https://ucris.univie.ac.at/portal/en/publications/globaltolocal-incompatibility-monogamy-of-entanglement-and-groundstate-dimerization(4704e1bb-aa92-470f-9424-ae8c1ade6191).html