Sound pumping in an alternating quantum spin chain

The pumping of the energy of a longitudinal sound by a quantum spin chain with the alternation of coupling constants is studied theoretically. It is shown that the power of the sound wave, absorbed by the dimerized spin chain, is zero in the dynamical regime, i.e., at times, smaller than relaxation times. In the steady-state regime, for times, larger than the relaxation time, the dimerized quantum spin chain can absorb the power of the sound. We have shown that the absorption of the sound exists when the frequency of the wave is between two threshold values, related to two critical fields, at which quantum phase transitions take place. Contrary, the calculated magnetic field dependence of the absorbed power of the sound does not clearly manifest two critical fields. Nevertheless, we have shown that it is possible to extract the information about the value of the field, at which the spin gap of low-lying excitations is closed, from the temperature dependence of the absorption of the longitudinal sound.