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Entanglement entropy for nonzero genus topologies

S. Santhosh Kumar1,*, Suman Ghosh2,†, and S. Shankaranarayanan1,‡

  • 1School of Physics, Indian Institute of Science Education and Research (IISER-TVM), Thiruvananthapuram 695 016, India
  • 2Department of Theoretical Sciences, S.N. Bose National Centre for Basic Sciences, Salt Lake, Kolkata 700 098, India

  • *santhu@iisertvm.ac.in
  • †suman.ghosh@boson.bose.res.in
  • ‡Corresponding author. shanki@iisertvm.ac.in
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Phys. Rev. D 89, 065019 – Published 17 March, 2014

DOI: https://doi.org/10.1103/PhysRevD.89.065019

Abstract

Over the last three decades, entanglement entropy has been obtained for quantum fields propagating in Genus-0 topologies (spheres). For scalar fields propagating in these topologies, it has been shown that the entanglement entropy scales as area. In the last few years, nontrivial topologies are increasingly relevant for different areas. For instance, in describing quantum phases, it has been realized that long-range entangled states are described by topological order. If quantum entanglement can plausibly provide explanation for these, it is then imperative to obtain entanglement entropy in these topologies. In this work, using two different methods, we explicitly show that the entanglement entropy scales as area of the Genus-1 geometry.

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Phys. Rev. D 89, 065019– Published 17 March, 2014
  • Received 28 January 2014

© 2014 American Physical Society

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