arXiv:1410.6530 · Journal of High Energy Physics

Entanglement entropy for relevant and geometric perturbations

Vladimir Rosenhaus, Michael Smolkin

Published Feb 1, 2015• 99 citations

Abstract

We continue the study of entanglement entropy for a QFT through a perturbative expansion of the path integral definition of the reduced density matrix. The universal entanglement entropy for a CFT perturbed by a relevant operator is calculated to second order in the coupling. We also explore the geometric dependence of entanglement entropy for a deformed planar entangling surface, finding surprises at second order.

DOI: 10.1007/jhep02(2015)015

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arXiv:1410.6530 · Journal of High Energy Physics

Entanglement entropy for relevant and geometric perturbations

Vladimir Rosenhaus, Michael Smolkin

Published Feb 1, 2015• 99 citations

arXiv HTML PDF

Abstract

DOI: 10.1007/jhep02(2015)015

Related papers

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We provide a framework for a perturbative evaluation of the reduced density matrix. The method is based on a path integral in the analytically continued spacetime. It suggests an alternative to the holographic and ‘standard’ replica trick calculations of entanglement entropy. We implement this method within solvable field theory examples to evaluate leading order corrections induced by small perturbations in the geometry of the background and entangling surface. Our findings are in accord with Solodukhin’s formula for the universal term of entanglement entropy for four dimensional CFTs.We provide a framework for a perturbative evaluation of the reduced density matrix. The method is based on a path integral in the analytically continued spacetime. It suggests an alternative to the holographic and ‘standard’ replica trick calculations of entanglement entropy. We implement this method within solvable field theory examples to evaluate leading order corrections induced by small perturbations in the geometry of the background and entangling surface. Our findings are in accord with Solodukhin’s formula for the universal term of entanglement entropy for four dimensional CFTs.

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Shape dependence of entanglement entropy in conformal field theories

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arXiv:1902.05058Feb 13, 20191 citation

We study universal features in the shape dependence of entanglement entropy in the vacuum state of a conformal field theory (CFT) on

{\mathrm{\mathbb{R}}}^{1,d-1}

. We consider the entanglement entropy across a deformed planar or spherical entangling surface in terms of a perturbative expansion in the infinitesimal shape deformation. In particular, we focus on the second order term in this expansion, known as the entanglement density. This quantity is known to be non-positive by the strong-subadditivity property. We show from a purely field theory calculation that the non-local part of the entanglement density in any CFT is universal, and proportional to the coefficient C T appearing in the two-point function of stress tensors in that CFT. As applications of our result, we prove the conjectured universality of the corner term coefficient

\frac{\sigma }{C_T}=\frac{\pi^2}{24}

in d = 3 CFTs, and the holographic Mezei formula for entanglement entropy across deformed spheres.

Δ=\frac{d+2}{2}

generates a logarithmic universal term to the entanglement entropy. As the smooth case, when the boundary CFT deformed by a relevant operator, we find that the entanglement entropy of singular surface also contains a new logarithmic term which is due to relevant perturbation of the conformal field theory, and depends on the scaling dimension of relevant operator. We also find for extended singular surfaces,

c_{n}\times R^{m}

, as well as logarithmic term, the new universal double logarithmic terms may appear depending on the scaling dimension of relevant operator and spacetime dimensions. These new terms are due to relevant perturbation of the boundary theory.