  We investigated the thermodynamic properties of the spin-1/2 one-dimensional
Heisenberg antiferromagnet KCuGaF6 by measuring the specific heat in magnetic
fields. When this compound is subjected to a uniform magnetic field H a
transverse staggered magnetic field h is induced in this compound owing to the
staggered component of the g tensor and the Dzyaloshinskii-Moriya interaction
with an alternating 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 // 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 // b, a quantum phase transition between gapless and gapped
ground states was observed.
