Physics – Condensed Matter – Strongly Correlated Electrons
Scientific paper
2010-06-29
Quantum Information and Computation Vol. 11, No. 7&8 (2011) pp. 0563 - 0573
Physics
Condensed Matter
Strongly Correlated Electrons
7 pages, 1 figure, revised version. Accepted for publication in QIC
Scientific paper
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 $\xi \gg 1$. 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.
Orus Roman
Wei Tzu-Chieh
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