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We study in this work the ground state entanglement properties of finite XXspin-1/2 chains with random couplings, using Jordan-Wigner transformation. Wedivide the system into two parts and study reduced density matrices (RDMs) ofits subsystems. Due to the free-fermion nature of the problem, the RDMs takethe form of that of a free fermion thermal ensemble. Finding spectrum of thecorresponding entanglement Hamiltonian and corresponding eigenvectors, andcomparing them with real space renormalization group (RSRG) treatment, weestablish the validity of the RSRG approach for entanglement in the limit ofstrong disorder, but also find its limitations when disorder is weak. In thelatter case our work provides a way to visualize the "effective spins" thatform long distance singlet pairs.

Entanglement spectrum and entangled modes of random XX spin chains