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Rényi divergences from Euclidean quenches

Journal of High Energy Physics volume 2020, Article number: 94 (2020) Cite this article

A preprint version of the article is available at arXiv.

Abstract

We study the generalisation of relative entropy, the Rényi divergence Dα(ρ∥ρβ) in 2d CFTs between an excited state density matrix ρ, created by deforming the Hamiltonian, and the thermal density matrix ρβ. Using the path integral representation of this quantity as a Euclidean quench, we obtain the leading contribution to the Rényi divergence for deformations by scalar primaries and by conserved holomorphic currents in conformal perturbation theory. Furthermore, we calculate the leading contribution to the Rényi divergence when the conserved current perturbations have inhomogeneous spatial profiles which are versions of the sine-square deformation (SSD). The dependence on the Rényi parameter (α) of the leading contribution have a universal form for these inhomogeneous deformations and it is identical to that seen in the Rényi divergence of the simple harmonic oscillator perturbed by a linear potential. Our study of these Rényi divergences shows that the family of second laws of thermodynamics, which are equivalent to the monotonicity of Rényi divergences, do indeed provide stronger constraints for allowed transitions compared to the traditional second law.

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Authors and Affiliations

  1. Centre for High Energy Physics, Indian Institute of Science, C.V. Raman Avenue, Bangalore, 560012, India

    Barsha G. Chowdhury & Justin R. David

  2. Mani L. Bhaumik Institute for Theoretical Physics, Department of Physics & Astronomy, University of California, Los Angeles, CA, 90095, USA

    Shouvik Datta

Authors
  1. Barsha G. Chowdhury
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  2. Shouvik Datta
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  3. Justin R. David
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Correspondence to Justin R. David.

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ArXiv ePrint: 1912.07210

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Chowdhury, B.G., Datta, S. & David, J.R. Rényi divergences from Euclidean quenches. J. High Energ. Phys. 2020, 94 (2020). https://doi.org/10.1007/JHEP04(2020)094

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  • DOI: https://doi.org/10.1007/JHEP04(2020)094

Keywords

  • Conformal Field Theory
  • Field Theories in Lower Dimensions
  • Higher Spin Symmetry