Renyi Entropies for Free Field Theories

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.

35 pages, 4 figures; v2 refs added, minor changes

References in corpus (11)

• Towards a derivation of holographic entanglement entropy
• On Renormalization Group Flows in Four Dimensions
• Holographic c-theorems in arbitrary dimensions
• Entanglement as a Probe of Confinement
• Entanglement entropy, conformal invariance and extrinsic geometry
• Holographic Calculations of Renyi Entropy
• Entanglement Entropy in the O(N) model
• Universal entanglement entropy in 2D conformal quantum critical points
• Entanglement entropy of critical spin liquids
• Entanglement Entropy of the Two-Dimensional Heisenberg Antiferromagnet
• Rényi entanglement entropies in quantum dimer models : from criticality to topological order

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