Rényi entropies for free field theories
By I. Klebanov, Silviu S. Pufu, S. Sachdev, B. Safdi. 2011
153 citations recorded by the source corpus.
A bstractRényi entropies Sq 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 Rényi entropies across Sd−1 may be extracted from the thermal partition functions of these theories on either (d + 1)-dimensional de Sitter space or $ \mathbb{R} \times {\mathbb{H}^d} $, where $ {\mathbb{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 S1×$ {\mathbb{H}^d} $, respectively. We calculate the Rényi 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 S3 and on S1 × $ {\mathbb{H}^2} $. Analogous calculations for massive free fields provide monotonic interpolating functions between the Rényi entropies at the Gaussian and the trivial fixed points. Finally, we discuss similar Rényi entropy calculations in d > 2.
Subfields: Atomic and Molecular Physics, and Optics, Geometry and Topology, Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/dd5fc1fa5669abed85c846847fd8300c6fa06168
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Citations in the corpus
- Entanglement entropy: Holography and renormalization group (2018, background): “…additional UV divergences whose coefficients depend on the opening angles (Bueno and Myers, 2015; Bueno et al., 2015; Casini and Huerta, 2007; Casini et al., 2009; Elvang and Hadjiantonis, 2015; Fradkin and Moore, 2006; Hirata and Takayanagi, 2007; Klebanov et al., 2012b; Myers and Singh, 2012b).”
- Entanglement entropy from a holographic viewpoint (2012, methodology): “This analysis has been generalized to calculate the Renyi entropy [55] (see also [56, 57]).”
- Mutual information and the F-theorem (2015, methodology): “This prescription, used in [60], is motivated by the corresponding holographic calculations [11–13].”