  One of the fundamental principles of statistical physics is that only partial
information about a system's state is required for its macroscopic description.
This is not only true for thermal ensembles, but also for the unconventional
ensemble, known as Generalized Gibbs Ensemble (GGE), that is expected to
describe the relaxation of integrable systems after a quantum quench. By
analytically studying the quench dynamics in a prototypical one-dimensional
critical model, the massless free bosonic field theory, we find evidence of a
novel type of equilibration characterized by the preservation of an enormous
amount of memory of the initial state that is accessible by local measurements.
In particular, we show that the equilibration retains memory of non-Gaussian
initial correlations, in contrast to the case of massive free evolution which
erases all such memory. The GGE in its standard form, being a Gaussian
ensemble, fails to predict correctly the equilibrium values of local
observables, unless the initial state is Gaussian itself. Our findings show
that the equilibration of a broad class of quenches whose evolution is
described by Luttinger liquid theory with an initial state that is non-Gaussian
in terms of the bosonic field, is not correctly captured by the corresponding
bosonic GGE, raising doubts about the validity of the latter in general
one-dimensional gapless integrable systems such as the Lieb-Liniger model. We
also propose that the same experiment by which the GGE was recently observed
[Langen et al., Science 348 (2015) 207-211] can also be used to observe its
failure, simply by starting from a non-Gaussian initial state.
