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Sharp entanglement thresholds in the logarithmic negativity of disjoint blocks in the transverse-field Ising chain
Max Planck Inst Phys Komplexer Syst, D-01187 Dresden, Germany..
Max Planck Inst Phys Komplexer Syst, D-01187 Dresden, Germany..
Indian Inst Technol, Dept Phys, Bombay 400076, Maharashtra, India..
KTH, School of Engineering Sciences (SCI), Physics, Condensed Matter Theory.ORCID iD: 0000-0003-3328-8525
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2018 (English)In: New Journal of Physics, ISSN 1367-2630, E-ISSN 1367-2630, Vol. 20, article id 083032Article in journal (Refereed) Published
Abstract [en]

Entanglement has developed into an essential concept for the characterization of phases and phase transitions in ground states of quantum many-body systems. In this work we use the logarithmic negativity to study the spatial entanglement structure in the transverse-field Ising chain both in the ground state and at nonzero temperatures. Specifically, we investigate the entanglement between two disjoint blocks as a function of their separation, which can be viewed as the entanglement analog of a spatial correlation function. We find sharp entanglement thresholds at a critical distance beyond which the logarithmic negativity vanishes exactly and thus the two blocks become unentangled, which holds even in the presence of long-ranged quantum correlations, i.e., at the system's quantum critical point. Using time-evolving block decimation, we explore this feature as a function of temperature and size of the two blocks and present a simple model to describe our numerical observations.

Place, publisher, year, edition, pages
Institute of Physics Publishing (IOPP), 2018. Vol. 20, article id 083032
Keywords [en]
ground states and nonzero temperature states of transverse-field Ising model, entanglement, logarithmic negativity, density matrices and partial transpose, entanglement threshold and sudden death of entanglement
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URN: urn:nbn:se:kth:diva-234598DOI: 10.1088/1367-2630/aad9baISI: 000442724300002Scopus ID: 2-s2.0-85053134016OAI: oai:DiVA.org:kth-234598DiVA, id: diva2:1248292
Funder
Knut and Alice Wallenberg Foundation
Note

QC 20180914

Available from: 2018-09-14 Created: 2018-09-14 Last updated: 2018-10-16Bibliographically approved

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Bardarson, Jens H.

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