Low dimensionality enhances quantum fluctuations, triggering novel states of quantum matter to emerge. In real materials, low dimensionality usually arises from spatially strongly anisotropic couplings. Here, we demonstrate a different mechanism: in two-dimensional systems with coupled alternating ferromagnetic (FM) and antiferromagnetic (AFM) spin-
1/2 chains, an applied magnetic field may drive a dimensional reduction. Under magnetic field, the FM chains polarize and stiffen, suppressing the propagation of transverse AFM fluctuations from one chain to another, and effectively induce one-dimensional behavior at low energies. For a model describing botallackite, Cu
2(OH)
3Br, quantum Monte Carlo dynamics show that beyond a critical magnetic field, the low-energy spectrum reduces to that of a one-dimensional AFM Heisenberg spin-
1/2 chain with field-dependent incommensurate two-spinon fluctuations, providing clear signatures for inelastic neutron scattering.
This paper presents an overview of the properties of magnetic insulators, with emphasis on quantum effects. In particular, the consequences of strong quantum fluctuations on the low-energy properties of a number of systems are reviewed: the occurrence of a spin gap in spin-1 chains and other low-dimensional magnets; the presence of low-lying singlet excitations in several frustrated magnets; the interplay of orbital and spin fluctuations in orbitally degenerate Mott insulators. This review is intended as a pedagogical introduction to the field, and the formalism has been kept at a minimal level.