Field-induced gap in Cu benzoate and otherS=12antiferromagnetic chains

Recent experiments on the $S=\frac{1}{2}$ antiferromagnetic chain compound, Cu benzoate, discovered an unexpected gap scaling as approximately the $\frac{2}{3}$ power of an applied magnetic field. A theory of this gap, based on an effective staggered field, orthogonal to the applied uniform field, resulting from a staggered gyromagnetic tensor and a Dzyaloshinskii-Moriya interaction, leading to a sine-Gordon quantum field theory, has been developed. Here we discuss many aspects of this subject in considerable detail, including a review of the $S=\frac{1}{2}$ chain in a uniform field, a spin-wave theory analysis of the uniform plus staggered field problem, exact amplitudes for the scaling of gap, staggered susceptibility and staggered magnetization with field or temperature, intensities of soliton and breather peaks in the structure function, and field and temperature dependence of the total susceptibility.