In this paper, we study the ground-state entanglement properties of finite XX spin-1/2 chains with random couplings using the Jordan-Wigner transformation. We divide the system into two parts and study the reduced density matrices (RDMs) of its subsystems. Due to the free-fermion nature of the problem, the RDMs take the form of that of a free-fermion thermal ensemble. Finding the spectrum of the corresponding entanglement Hamiltonian and corresponding eigenvectors and comparing them with the real-space renormalization-group (RSRG) treatment, we establish the validity of the RSRG approach for entanglement in the limit of strong disorder but also find its limitations when disorder is weak. In the latter case, our paper provides a way to visualize the “effective spins” that form long-distance singlet pairs.
