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Entanglement Entropy in Critical Quantum Spin Chains with Boundaries and Defects

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Entanglement in Spin Chains

Part of the book series: Quantum Science and Technology ((QST))

Abstract

Entanglement entropy (EE) in critical quantum spin chains described by 1+ 1D conformal field theories contains signatures of the universal characteristics of the field theory. Boundaries and defects in the spin chain give rise to universal contributions in the EE. In this work, we analyze these universal contributions for the critical Ising and XXZ spin chains for different conformal boundary conditions and defects. For the spin chains with boundaries, we use the boundary states for the corresponding continuum theories to compute the subleading contribution to the EE analytically and provide supporting numerical computation for the spin chains. Subsequently, we analyze the behavior of EE in the presence of conformal defects for the two spin chains and describe the change in both the leading logarithmic and subleading terms in the EE.

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Notes

  1. 1.

    See Ref. [16] for discussion on different boundary conditions at the two ends.

  2. 2.

    Note that the open chain can be obtained from the periodic Ising chain by introducing an energy defect between the sites L and 1 with strength b𝜖 = 0.

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Acknowledgements

We are particularly grateful to David Rogerson and Frank Pollmann for numerous discussions and collaboration on a related project. AR is supported by a grant from the Simons Foundation (825876, TDN). HS is supported by the ERC Advanced Grant NuQFT.

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Authors and Affiliations

  1. Department of Physics and Astronomy, Rutgers University, Piscataway, NJ, USA

    Ananda Roy

  2. Institut de Physique Théorique, Paris Saclay University, CEA, CNRS, Gif-sur-Yvette, France

    Hubert Saleur

  3. Department of Physics and Astronomy, University of Southern California, Los Angeles, CA, USA

    Hubert Saleur

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  1. Ananda Roy
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  2. Hubert Saleur
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Correspondence to Ananda Roy .

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Editors and Affiliations

  1. Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu, China

    Abolfazl Bayat

  2. Department of Physics and Astronomy, University College London, London, UK

    Sougato Bose

  3. Department of Physics, University of Gothenburg, Göteborg, Sweden

    Henrik Johannesson

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Roy, A., Saleur, H. (2022). Entanglement Entropy in Critical Quantum Spin Chains with Boundaries and Defects. In: Bayat, A., Bose, S., Johannesson, H. (eds) Entanglement in Spin Chains. Quantum Science and Technology. Springer, Cham. https://doi.org/10.1007/978-3-031-03998-0_3

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