Entanglement entropy of the random s=1 Heisenberg chain

Random spin chains at quantum critical points exhibit an entanglement entropy between a segment of length L and the rest of the chain that scales as log(2) L with a universal coefficient. Since for pure quantum critical spin chains this coefficient is fixed by the central charge of the associated conformal field theory, the universal coefficient in the random case can be understood as an effective central charge. In this paper we calculate the entanglement entropy and effective central charge of the spin-1 random Heisenberg model in its random-singlet phase and also at the critical point at which the Haldane phase breaks down. The latter is the first entanglement calculation for an infinite-randomness fixed point that is not in the random-singlet universality class. Our results are consistent with a c-theorem for flow between infinite-randomness fixed points. The formalism we use can be generally applied to calculation of quantities that depend on the RG history in s >= 1 random Heisenberg chains.