Random-singlet phases beyond one spatial dimension

When the linear Heisenberg spin chain is given non-uniform exhange couplings, its ground state becomes frozen in a quasi-static singlet bond pattern. This so-called random-singlet phase has long been understood via a renormalization-group (RG) procedure that decimates the bonds from strongest to weakest; the flow equations indicate that even infinitesimal disorder drives the system toward an infinite-randomness fixed point. We present an non-RG construction, based on the large-$N$ limit of SU($N$), that reproduces the linear-chain result, but which also generalizes to lattices in higher spatial dimension. Beyond a threshold in disorder $D$ and rank $N$, a random-singlet phase exists and exhibits spin correlations that decay algebraically with characteristic exponents. The predictions in two and three dimensions are verified using Quantum Monte Carlo.