We study the entanglement properties of random XX spin 1/2 chains at an arbitrary temperature T using random partitioning, where sites of a size-varying subsystem are chosen randomly with a uniform probability p, and then an average over subsystem pos- sibilities is taken. We show analytically and numerically, using the approximate method of real space renormalization group, that random partitioning entanglement entropy for the XX spin chain of size L behaves like EE(T , p) = a(T , p)L at an arbitrary tem- perature T with a uniform probability p, i.e., it obeys volume law. We demonstrate that a(T , p) = ln(2)⟨Ps +Pt↑↓ ⟩p(1−p), where Ps and Pt↑↓ are the average probabilities of having singlet and triplet↑↓ in the entire system, respectively. We also study the temperature dependence of pre-factor a(T , p). We show that EE with random partitioning reveals both short- and long-range correlations in the entire system.
