2011/11/30 by Igor R. Klebanov, Silviu S. Pufu, Subir Sachdev +1
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Quantum many-body systems #cond-mat.stat-mech #hep-th #quant-ph
paper · pdf · doi:10.1007/jhep04(2012)074
published as JHEP 1204 (2012) 074 · 35 pages, 4 figures; v2 refs added, minor changes
arxiv created 2012/03/01 · openalex publication_date 2012/04/01 · arxiv updated 2012/05/15 · openalex created_date 2020/04/17 · openalex updated_date 2026/07/28
Renyi 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 Renyi entropies across Sd-1 may be extracted from the thermal partition functions of these theories on either (d+1)-dimensional de Sitter space or R x Hd, where Hd 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 x Hd, 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 S3 and on S1 x H2. 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.