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arXiv · 1111.6290

Renyi Entropies for Free Field Theories

Igor R. Klebanov·Silviu S. Pufu·Subir Sachdev·Benjamin R. Safdi
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Abstract

Renyi entropies S_q are useful measures of quantum entanglement; they can be calculated from traces of the reduced density matrix raised to power q, with q>=0. For (d+1)-dimensional conformal field theories, the Renyi entropies across S^{d-1} may be extracted from the thermal partition functions of these theories on either (d+1)-dimensional de Sitter space or R x H^d, where H^d is the d-dimensional hyperbolic space. These thermal partition functions can in turn be expressed as path integrals on branched coverings of the (d+1)-dimensional sphere and S^1 x H^d, respectively. We calculate the Renyi entropies of free massless scalars and fermions in d=2, and show how using zeta-function regularization one finds agreement between the calculations on the branched coverings of S^3 and on S^1 x H^2. Analogous calculations for massive free fields provide monotonic interpolating functions between the Renyi entropies at the Gaussian and the trivial fixed points. Finally, we discuss similar Renyi entropy calculations in d>2.

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Igor R. Klebanov, Silviu S. Pufu, Subir Sachdev, Benjamin R. Safdi. 2012-03-01. Renyi Entropies for Free Field Theories. https://doi.org/10.1007/jhep04(2012)074

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