We investigated the thermodynamic properties of the spin-1/2 one-dimensional Heisenberg antiferromagnet KCuGaF
6 by measuring the specific heat in magnetic fields. When this compound is subjected to a uniform magnetic field $\mathbit{H}$, a transverse staggered magnetic field $\mathbit{h}$ is induced in this compound owing to the staggered component of the $\mathbit{g}$ tensor and the Dzyaloshinskii-Moriya interaction with an alternating $\mathbit{D}$ vector. Consequently, the quantum sine-Gordon (SG) model is an effective model of this compound in a uniform magnetic field. In three different field directions, we observed a magnetic-field-induced gap, which increases with
H. We analyzed experimental results using specific heat theory based on quantum SG theory. The thermodynamic property for $H\phantom{\rule{0.16em}{0ex}}\ensuremath{\parallel}\phantom{\rule{0.16em}{0ex}}c$ is very well described in terms of the elementary excitations characteristic of the quantum SG model, while for the other field directions significant contributions from other excitation modes beyond the framework of the quantum SG model were observed. For $H\phantom{\rule{0.16em}{0ex}}\ensuremath{\parallel}\phantom{\rule{0.16em}{0ex}}b$, a quantum phase transition between gapless and gapped ground states was observed.
We investigate the amplitude (Higgs) mode associated with longitudinal fluctuations of the order parameter at the continuous spontaneous symmetry breaking phase transition. In quantum magnets, due to the fast decay of the amplitude mode into low-energy Goldstone excitations, direct observation of this mode represents a challenging task. By focusing on a quasi-one-dimensional geometry, we circumvent the difficulty and investigate the amplitude mode in a system of weakly coupled spin chains with the help of quantum Monte Carlo simulations, stochastic analytic continuation, and a chain-mean field approach combined with a mapping to the field-theoretic sine-Gordon model. The amplitude mode is observed to emerge in the longitudinal spin susceptibility in the presence of a weak symmetry-breaking staggered field. A conventional measure of the amplitude mode in higher dimensions, the singlet bond mode, is found to appear at a lower than the amplitude mode frequency. We identify these two excitations with the second (first) breather of the sine-Gordon theory, correspondingly. In contrast to higher-dimensional systems, the amplitude and bond order fluctuations are found to carry significant spectral weight in the quasi-1D limit.