Universal geometric entanglement close to quantum phase transitions

Orus, Roman (2008) Universal geometric entanglement close to quantum phase transitions. Physical Review Letters, 100 13: Article Number: 130502. doi:10.1103/PhysRevLett.100.130502

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Author Orus, Roman
Title Universal geometric entanglement close to quantum phase transitions
Journal name Physical Review Letters   Check publisher's open access policy
ISSN 0031-9007
Publication date 2008-04-04
Sub-type Article (original research)
DOI 10.1103/PhysRevLett.100.130502
Open Access Status File (Publisher version)
Volume 100
Issue 13
Start page Article Number: 130502
Total pages 4
Editor G. Basbas
J. Sandweiss
R. B. Schuhmann
S. G. Brown
Place of publication College Park, Maryland, USA
Publisher American Physical Society
Collection year 2009
Language eng
Subject C1
970102 Expanding Knowledge in the Physical Sciences
020603 Quantum Information, Computation and Communication
Formatted abstract
 Under successive renormalization group transformations applied to a quantum state |Ψ > of finite correlation length ξ, there is typically a loss of entanglement after each iteration. How good it is then to replace |Ψ> by a product state at every step of the process? In this Letter we give a quantitative answer to this question by providing first analytical and general proofs that, for translationally invariant quantum systems in one spatial dimension, the global geometric entanglement per region of size L>> ξ diverges with the correlation length as (c/12)log(ξ /ε)  close to a quantum critical point with central charge c, where ε is a cutoff at short distances. Moreover, the situation at criticality is also discussed and an upper bound on the critical global geometric entanglement is provided in terms of a logarithmic function of L.
Keyword Spin Chains
Q-Index Code C1
Q-Index Status Confirmed Code

Document type: Journal Article
Sub-type: Article (original research)
Collections: 2009 Higher Education Research Data Collection
School of Mathematics and Physics
 
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Citation counts: TR Web of Science Citation Count  Cited 61 times in Thomson Reuters Web of Science Article | Citations
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Created: Fri, 13 Mar 2009, 15:47:38 EST by Jo Hughes on behalf of School of Mathematics & Physics