We study the moments of the partial transpose of the reduced density matrix of two intervals for the free massless Dirac fermion. By means of a direct calculation based on a coherent state path integral, we find an analytic form for these moments in terms of the Riemann theta function. We show that moments of arbitrary order are equal to the same quantities for the compactified boson at the self-dual point. These equalities also imply the nontrivial result that the negativity of the free fermion and the self-dual boson are equal.

Towards the entanglement negativity of two disjoint intervals for a one dimensional free fermion / Coser, Andrea; Tonni, Erik; Calabrese, Pasquale. - In: JOURNAL OF STATISTICAL MECHANICS: THEORY AND EXPERIMENT. - ISSN 1742-5468. - 2016:3(2016), pp. 1-28. [10.1088/1742-5468/2016/03/033116]

Towards the entanglement negativity of two disjoint intervals for a one dimensional free fermion

Coser, Andrea;Tonni, Erik;Calabrese, Pasquale
2016

Abstract

We study the moments of the partial transpose of the reduced density matrix of two intervals for the free massless Dirac fermion. By means of a direct calculation based on a coherent state path integral, we find an analytic form for these moments in terms of the Riemann theta function. We show that moments of arbitrary order are equal to the same quantities for the compactified boson at the self-dual point. These equalities also imply the nontrivial result that the negativity of the free fermion and the self-dual boson are equal.
2016
3
1
28
033116
https://arxiv.org/abs/1508.00811
http://cdsads.u-strasbg.fr/abs/2016JSMTE..03.3116C
Coser, Andrea; Tonni, Erik; Calabrese, Pasquale
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.11767/32846
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