Entanglement in fermionic chains with finite range coupling and broken symmetries
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 contiguous sites in the limit of large . 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 . 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.
Cite
@article{arxiv.1506.06665,
title = {Entanglement in fermionic chains with finite range coupling and broken symmetries},
author = {F. Ares and J. G. Esteve and F. Falceto and A. R. de Queiroz},
journal= {arXiv preprint arXiv:1506.06665},
year = {2015}
}
Comments
27 pages, 5 figures