  We numerically investigate the low-lying entanglement spectrum of the ground
state of random one-dimensional spin chains obtained after partition of the
chain into two equal halves. We consider two paradigmatic models: the spin-1/2
random transverse field Ising model, solved exactly, and the spin-1 random
Heisenberg model, simulated using the density matrix renormalization group. In
both cases we analyze the mean Schmidt gap, defined as the difference between
the two largest eigenvalues of the reduced density matrix of one of the two
partitions, averaged over many disorder realizations. We find that the Schmidt
gap detects the critical point very well and scales with universal critical
exponents.
