  In this work, we address the recent experiment [S. Tewari et al.,
arXiv:1503.05057v1], where the suppression of phase coherence of a
single-electron wave packet created at the edge of a quantum Hall (QH) system
at filling factor 2 has been investigated with the help of an electronic
Mach-Zehnder (MZ) interferometer. The authors of the experiment have observed
an unexpected behavior of phase coherence, that saturates at high energies
instead of vanishing, presumably suggesting the relaxation of a wave packet to
the ground state before it arrives to the MZ interferometer. Here, we
theoretically investigate this situation using the model of edge states [I. P.
Levkivskyi, E. V. Sukhorukov, Phys. Rev. B 78, 045322 (2008)], which accounts
for the strong Coulomb interaction between the two electron channels at the
edge of a QH system. We conclude that the observed phenomenon cannot be
explained within this model for the reason that under an assumption of
linearity of the electron spectrum at low energies the system remains
integrable in terms of the collective charge excitations, and therefore full
relaxation to the ground state is not possible, despite strong interactions. As
a result, the degree of the phase coherence decreases with energy of the
initial state in a power-law manner. Since this does not happen in the
experiment, a new physical phenomenon may take place at the edge of a QH state,
which deserves further investigations. We support our findings by calculating
the energy distribution and the Wigner function of the outgoing non-equilibrium
state of the single-electron wave packet.
