Figure 2

(a) Exact Rényi entropy S _α (blue dots) vs. its asymptotic approximation (24) (continuous red line) for a subsystem consisting of three equispaced blocks of equal length N/12 when the whole system’s state (2) is made up of a sequence of consecutive excited modes of length N/12 (r = 3, s = 1, γ _x  = 1/4, γ _p  = 1/12). The values of the Rényi parameter α considered are (from top to bottom) 1/2, 3/5, 3/4, 1, 3/2, 2 and 3. (b) Difference ε between the exact entropy S ₃ and its approximation (24) in the previous configuration as a function of the number of fermions N. The continuous red line is the graph of the function f(N)N ^−2/3, with f(N) = −5.54238cos(ν ₀ N) − 0.742586cos(3ν ₀ N) − 0.39794cos(5ν ₀ N) and ν ₀ = 2πγ _x γ _p /r = π/72.