Rényi divergences from Euclidean quenches

Chowdhury, Barsha G. ; Datta, Shouvik ; David, Justin R. (2020) Rényi divergences from Euclidean quenches Journal of High Energy Physics, 2020 (4). ISSN 1029-8479

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

Related URL: http://dx.doi.org/10.1007/JHEP04(2020)094


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.

Item Type:Article
Source:Copyright of this article belongs to Springer Nature Switzerland AG.
Keywords:Conformal Field Theory; Field Theories in Lower Dimensions; Higher Spin Symmetry.
ID Code:116987
Deposited On:14 Apr 2021 08:04
Last Modified:14 Apr 2021 08:04

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