Entanglement equipartition in critical random spin chains

Abstract: The reduced density matrix of many-body systems possessing an additive conserved quantity can be decomposed in orthogonal sectors which can be independently analyzed. Recently, these have been proven to equally contribute to entanglement entropy for one dimensional conformal and integrable systems. In this paper, we extend this equipartition theorem to the disordered critical systems by studying the random singlet phase. We analytically compute the disorder averaged symmetry resolved R\'enyi entropies and show the leading orders are independent of the symmetry sector. Our findings are cross-checked with simulations within the numerical strong disorder renormalization group. We also identify the first subleading term breaking equipartition which is of the form $s^2/\ln\ell$ where $s$ is the magnetization of a subsystem of length $\ell$.