  We investigate the spatially anisotropic square lattice quantum
antiferromagnet. The model describes isotropic spin-1/2 Heisenberg chains
(exchange constant J) coupled antiferromagnetically in the transverse (J_\perp)
and diagonal (J_\times), with respect to the chain, directions. Classically,
the model admits two ordered ground states -- with antiferromagnetic and
ferromagnetic inter-chain spin correlations -- separated by a first order phase
transition at J_\perp=2J_\times. We show that in the quantum model this
transition splits into two, revealing an intermediate quantum-disordered
columnar dimer phase, both in two dimensions and in a simpler two-leg ladder
version. We describe quantum-critical points separating this spontaneously
dimerized phase from classical ones.
