Solitons and spinons in the quantum sine-gordon spin chain

An isotropic S = 1/2 Heisenberg antiferromagnetic (AFM) chain with uniform nearest-neighbor exchange coupling represents one of the paradigm models of quantum magnetism. Its ground state is a spin singlet, and the dynamics are determined by a gapless two-particle continuum of spin- 1/2 excitations, commonly referred to as spinons. Since the S = 1/2 AFM chain is critical, even small perturbations can considerably change fundamental properties of the system. One of the most prominent examples is the S = 1/2 AFM chain perturbed by an alternating g-tensor and the Dzyaloshinskii-Moriya interaction; this situation is realized experimentally in the copper pyrimidine dinitrate, Cu-PM. In the presence of such interactions, application of a uniform external field H induces an effective transverse staggered field h / H, which leads to the opening of an energy gap ¢ / H2=3. Here we report on the excitation spectrum in Cu-PM measured using submillimeter wave electron spin resonance (ESR) spectroscopy in fields up to 25 T [1]. Ten excitation modes are resolved in the low-temperature spectrum. The field-induced gap is measured directly. Signatures of three breather branches and a soliton, as well as those of several multi-particle excitation modes are identified. The experimental data are sufficiently detailed to make a very accurate comparison with predictions based on the quantum sine-Gordon field theory [2]. In addition, a new theoretical concept proposed recently by Oshikawa and Affleck [3] has been tested. Their theory, based on bosonization and the self-energy formalism, can be applied for precise calculation of ESR parameters of S = 1/2 AFM chains in the perturbative spinon regime. Excellent quantitative agreement between the theoretical predictions and experiment is obtained [4].