Towards the entanglement negativity of two disjoint intervals for a one dimensional free fermion
Andrea CoserSISSA and INFN, via Bonomea 265, 34136 Trieste, ItalyErik TonniSISSA and INFN, via Bonomea 265, 34136 Trieste, ItalyPasquale CalabreseSISSA and INFN, via Bonomea 265, 34136 Trieste, Italy
2016en
ABI
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 coherent state path integral, we find an analytic form for these moments in terms of the Riemann theta function. We show that the moments of arbitrary order are equal to the same quantities for the compactified boson at the self-dual point. These equalities imply the non trivial result that also the negativity of the free fermion and the self-dual boson are equal.
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Cited by 20 references