On numerical calculation of Renyi entropy for a sphere

We numerically compute the Renyi entropy for four-dimensional free scalar field theory with a spherical entangling surface. As is well known, the Renyi entropy as a function of the boundary area exhibits linear dependence in the leading order. The coefficient of the subleading logarithmic term from our numerical data, as a function of the Renyi order q, agrees nicely with the general prediction of conformal field theory computation. The motivation of this work is also partly to see how the efficiency of numerical computation changes as a function of q. For q < 1 the summation over eigenvalues of reduced density matrix takes longer since the series converges more slowly than for q = 1. For q > 1 the convergence is faster, but the relative error becomes large as a general trend. (C) 2014 The Author. Published by Elsevier B.V.