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Title:
Entanglement in fermionic chains with finite range coupling and with complex coupling
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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. A striking new feature of our formula for the entanglement entropy is the appearance of a term scaling with the logarithmic of the size of X. This logarithmic behaviour originates from certain discontinuities in the symbol of the block Toeplitz matrix. This formula is relevant for the XY spin model with Dzyaloshinski-Moriya coupling.
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