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 $X$ 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.

27 pages, 5 figures

References in corpus (7)

• Kitaev chains with long-range pairing
• Entanglement and Particle Identity: A Unifying Approach
• Entanglement, Particle Identity and the GNS Construction: A Unifying Approach
• Entanglement entropy in quantum spin chains with finite range interaction
• Entropy of XY Spin Chain and Block Toeplitz Determinants
• Entanglement of several blocks in fermionic chains
• Random matrix theory and critical phenomena in quantum spin chains

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