Entanglement entropy of two disjoint intervals in c=1 theories

Journal of Statistical Mechanics Theory and Experiment (Impact Factor: 2.06). 03/2011; 6(06). DOI: 10.1088/1742-5468/2011/06/P06012
Source: arXiv

ABSTRACT We study the scaling of the Renyi entanglement entropy of two disjoint blocks
of critical lattice models described by conformal field theories with central
charge c=1. We provide the analytic conformal field theory result for the
second order Renyi entropy for a free boson compactified on an orbifold
describing the scaling limit of the Ashkin-Teller (AT) model on the self-dual
line. We have checked this prediction in cluster Monte Carlo simulations of the
classical two dimensional AT model. We have also performed extensive numerical
simulations of the anisotropic Heisenberg quantum spin-chain with tree-tensor
network techniques that allowed to obtain the reduced density matrices of
disjoint blocks of the spin-chain and to check the correctness of the
predictions for Renyi and entanglement entropies from conformal field theory.
In order to match these predictions, we have extrapolated the numerical results
by properly taking into account the corrections induced by the finite length of
the blocks to the leading scaling behavior.

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Available from: Luca Tagliacozzo, Aug 15, 2015
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    • "Here c is the central charge of the conformal field theory, c 1 a non-universal constant, while L and L A are the sizes of the full system and of part A, respectively. Universal information can also be extracted from the entanglement between many disjoint blocks [50] [51] [52] [53] [54] [55] [56] [57] [58] [59] [60] [61] [62], or from the scaling corrections of the von Neumann entropy [63] [64] [65] [66] [67] [68] [69]. "
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    • "Unfortunately, the analytic continuation that allows to obtain I(A 1 , A 2 ) is not known in general but only in some limiting regimes. Detailed studies of I(A 1 , A 2 ) for spin chain models have also been done [19] [20] [21] [22]. "
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