  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.
