Geometric entanglement of one-dimensional systems: bounds and scalings in the thermodynamic limit

Orús, Román and Wei, Tzu-Chieh (2011) Geometric entanglement of one-dimensional systems: bounds and scalings in the thermodynamic limit. Quantum Information and Computation, 11 7-8: 563-573.

Author Orús, Román
Wei, Tzu-Chieh
Title Geometric entanglement of one-dimensional systems: bounds and scalings in the thermodynamic limit
Journal name Quantum Information and Computation
ISSN 1533-7146
Publication date 2011-07-01
Sub-type Article (original research)
Open Access Status
Volume 11
Issue 7-8
Start page 563
End page 573
Total pages 11
Place of publication Paramus, NJ, United States
Publisher Rinton Press
Language eng
Subject 2614 Theoretical Computer Science
1703 Computational Theory and Mathematics
3100 Physics and Astronomy
3109 Statistical and Nonlinear Physics
2610 Mathematical Physics
3106 Nuclear and High Energy Physics
Formatted abstract
In this paper the geometric entanglement (GE) of systems in one spatial dimension (1D) and in the thermodynamic limit is analyzed focusing on two aspects. First, we reexamine the calculation of the GE for translation-invariant matrix product states (MPSs) in the limit of infinite system size. We obtain a lower bound to the GE which collapses to an equality under certain sufficient conditions that are fulfilled by many physical systems, such as those having unbroken space (P) or space-time (PT) inversion symmetry. Our analysis justifies the validity of several derivations carried out in previous works. Second, we derive scaling laws for the GE per site of infinite-size 1D systems with correlation length ξ » 1. In the case of MPSs, we combine this with the theory of finite-entanglement scaling, allowing to understand the scaling of the GE per site with the MPS bond dimension at conformally invariant quantum critical points.
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status UQ
Additional Notes Communicated by : R Jozsa & M Mosca.

Document type: Journal Article
Sub-type: Article (original research)
Collection: School of Mathematics and Physics
 
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