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Entanglement entropy of a massive fermion on a torus

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Abstract

The Rényi entropies of a massless Dirac fermion on a circle with chemical potential are calculated analytically at nonzero temperature by using the bosonization method. The bosonization of a massive Dirac fermion to the sine-Gordon model lets us obtain the small mass corrections to the entropies. We numerically compute the Rényi entropies by putting a massive fermion on the lattice and find agreement between the analytic and numerical results. In the presence of a mass gap, we show that corrections to Rényi and entanglement entropies in the limit m gap ≫ T scale as \( {e^{{{{{-{m_{\mathrm{gap}}}}} \left/ {T} \right.}}}} \). We also show that when there is ground state degeneracy in the gapless case, the limits m gap → 0 and T → 0 do not commute.

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Authors and Affiliations

  1. C.N. Yang Institute for Theoretical Physics, Stony Brook University, Stony Brook, NY, 11794, U.S.A.

    Christopher P. Herzog

  2. Department of Physics, Princeton University, Princeton, NJ, 08544, U.S.A.

    Tatsuma Nishioka

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  1. Christopher P. Herzog
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  2. Tatsuma Nishioka
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Correspondence to Tatsuma Nishioka.

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ArXiv ePrint: 1301.0336

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Herzog, C.P., Nishioka, T. Entanglement entropy of a massive fermion on a torus. J. High Energ. Phys. 2013, 77 (2013). https://doi.org/10.1007/JHEP03(2013)077

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  • DOI: https://doi.org/10.1007/JHEP03(2013)077

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