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Rényi divergences from Euclidean quenches

Chowdhury, BG and Datta, S and David, JR (2020) Rényi divergences from Euclidean quenches. In: Journal of High Energy Physics, 2020 (4).

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Official URL: https://dx.doi.org/ 10.1007/JHEP04(2020)094


We study the generalisation of relative entropy, the Rényi divergence Dα(���β) in 2d CFTs between an excited state density matrix �, created by deforming the Hamiltonian, and the thermal density matrix �β. 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. © 2020, The Author(s).

Item Type: Journal Article
Publication: Journal of High Energy Physics
Publisher: Springer
Additional Information: Copy right for this article belongs to Springer
Keywords: Conformal Field Theory, Field Theories in Lower Dimensions, Higher Spin Symmetry
Department/Centre: Division of Physical & Mathematical Sciences > Centre for High Energy Physics
Date Deposited: 19 Oct 2020 05:40
Last Modified: 19 Oct 2020 05:40
URI: http://eprints.iisc.ac.in/id/eprint/65291

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