Negativity for two blocks in the one-dimensional spin-1 Affleck-Kennedy-Lieb-Tasaki model

Journal Article · Thu Dec 15 04:00:00 EST 2011 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.84.062307· OSTI ID:22095567

Santos, Raul A.; Korepin, V.; Bose, Sougato ^[1]

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1. C. N. Yang Institute for Theoretical Physics, Stony Brook University, Stony Brook, New York 11794-3840 (United States)

In this paper we compute the entanglement, as quantified by negativity, between two blocks of length L{sub A} and L{sub B}, separated by L sites in the one-dimensional spin-1 Affleck-Kennedy-Lieb-Tasaki (AKLT) model. We took the model with two different boundary conditions. We consider the case of N spin-1 particles in the bulk and one spin-1/2 particle at each boundary, which constitute a unique ground state, and the case of just spin 1, even at the end of the chain, where the degeneracy of the ground state is 4. In both scenarios we made a partition consisting of two blocks A and B, containing L{sub A} and L{sub B} sites, respectively. The separation of these two blocks is L. In both cases we explicitly obtain the reduced density matrix of the blocks A and B. We prove that the negativity in the first case vanishes identically for L{>=}1, while in the second scenario it may approach a constant value N=1/2 for each degenerate eigenstate depending on the way one constructs these eigenstates. However, as there is some freedom in constructing these eigenstates, vanishing entanglement is also possible in the latter case. Additionally, we also compute the entanglement between noncomplementary blocks in the case of periodic boundary conditions for the spin-1 AKLT model for which there is a unique ground state. Even in this case, we find that the negativity of separated blocks of spins is zero.

• OSTI ID: 22095567
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 6 Vol. 84; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BOSONS
BOUNDARY CONDITIONS
DENSITY MATRIX
EIGENSTATES
FERMIONS
GROUND STATES
ONE-DIMENSIONAL CALCULATIONS
PARTITION
PERIODICITY
QUANTUM ENTANGLEMENT
QUANTUM MECHANICS
QUANTUM STATES
SPIN