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arXiv · 1506.06665

Entanglement in fermionic chains with finite range coupling and broken symmetries

F. Ares·J. G. Esteve·F. Falceto·A. R. de Queiroz
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Abstract

We obtain a formula for the determinant of a block Toeplitz matrix associated with a quadratic fermionic chain with complex coupling. Such couplings break reflection symmetry and/or charge conjugation symmetry. We then apply this formula to compute the Renyi entropy of a partial observation to a subsystem consisting of $X$ contiguous sites in the limit of large $X$. The present work generalizes similar results due to Its, Jin, Korepin and Its, Mezzadri, Mo. A striking new feature of our formula for the entanglement entropy is the appearance of a term scaling with the logarithm of the size of $X$. This logarithmic behaviour originates from certain discontinuities in the symbol of the block Toeplitz matrix. Equipped with this formula we analyse the entanglement entropy of a Dzyaloshinski-Moriya spin chain and a Kitaev fermionic chain with long range pairing.

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F. Ares, J. G. Esteve, F. Falceto, A. R. de Queiroz. 2015-06-22. Entanglement in fermionic chains with finite range coupling and broken symmetries. https://doi.org/10.1103/physreva.92.042334

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