Universal corrections to scaling for block entanglement in spin-1/2<i>XX</i>chains
Pasquale CalabreseDipartimento di Fisica, dell’Università di Pisa and INFN, Pisa, ItalyFabian H. L. EßlerThe Rudolf Peierls Centre for Theoretical Physics, Oxford University, Oxford OX1 3NP, UK
2010en
ABI
Abstract
We consider the Renyi entropies S(n)(l) in the one-dimensional spin1/ 2 Heisenberg XX chain in a magnetic field. The case n = 1 corresponds to the von Neumann 'entanglement' entropy. Using a combination of methods based on the generalized Fisher Hartwig conjecture and a recurrence relation connected to the Painleve e VI differential equation we obtain the asymptotic behaviour, accurate to order O(l(-3)), of the Renyi entropies S(n)(l) for large block lengths l. For n = 1, 2, 3, 10 this constitutes the 3, 6, 10, 48 leading terms respectively. The o(1) contributions are found to exhibit a rich structure of oscillatory behaviour, which we analyse in some detail both for finite n and in the limit n ->infinity.
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