Middle-field cusp singularities in the magnetization process of one-dimensional quantum antiferromagnets

We study the zero-temperature magnetization process $(M-H$ curve) of one-dimensional quantum antiferromagnets using a variant of the density-matrix renormalization group method. For both the $S=1/2\mathrm{}$ zig-zag spin ladder and the $S=1\mathrm{}$ bilinear-biquadratic chain, we find clear cusp-type singularities in the middle-field region of the $M-H$ curve. These singularities are successfully explained in terms of the double-minimum shape of the energy dispersion of the low-lying excitations. For the $S=1/2\mathrm{}$ zig-zag spin ladder, we find that the cusp formation accompanies the Fermi-liquid to non-Fermi-liquid transition.