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Bi-partite Entanglement Entropy in Massive QFT with a Boundary: the Ising Model

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Abstract

In this paper we give an exact infinite-series expression for the bi-partite entanglement entropy of the quantum Ising model in the ordered regime, both with a boundary magnetic field and in infinite volume. This generalizes and extends previous results involving the present authors for the bi-partite entanglement entropy of integrable quantum field theories, which exploited the generalization of the form factor program to branch-point twist fields. In the boundary case, we isolate in a universal way the part of the entanglement entropy which is related to the boundary entropy introduced by Affleck and Ludwig, and explain how this relation should hold in more general QFT models. We provide several consistency checks for the validity of our form factor results, notably, the identification of the leading ultraviolet behaviour both of the entanglement entropy and of the two-point function of twist fields in the bulk theory, to a great degree of precision by including up to 500 form factor contributions.

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Authors and Affiliations

  1. Centre for Mathematical Science, City University London, Northampton Square, London, EC1V 0HB, UK

    Olalla A. Castro-Alvaredo

  2. Department of Mathematical Sciences, Durham University, South Road, Durham, DH1 3LE, UK

    Benjamin Doyon

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  1. Olalla A. Castro-Alvaredo
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  2. Benjamin Doyon
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Correspondence to Olalla A. Castro-Alvaredo.

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Castro-Alvaredo, O.A., Doyon, B. Bi-partite Entanglement Entropy in Massive QFT with a Boundary: the Ising Model. J Stat Phys 134, 105–145 (2009). https://doi.org/10.1007/s10955-008-9664-2

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  • DOI: https://doi.org/10.1007/s10955-008-9664-2

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