  We address the question of the stability of the (fractional) quantum Hall
effect (QHE) in presence of pseudomagnetic disorder generated by mechanical
deformations of a graphene sheet. Neglecting the potential disorder and taking
into account only strain-induced random pseudomagnetic fields, it is possible
to write down a Laughlin-like trial ground-state wave function explicitly.
Exploiting the Laughlin plasma analogy, we demonstrate that in the case of
fluctuating pseudomagnetic fluxes of relatively small amplitude both the
integer and fractional quantum Hall effects are always stable upon the
deformations. By contrast, in the case of bubble-induced pseudomagnetic fields
in graphene on a substrate (a small number of large fluxes) the disorder can be
strong enough to cause a glass transition in the corresponding classical
Coulomb plasma, resulting in the destruction of fractional quantum Hall regime
and in a quantum phase transition to a non-ergodic state of the lowest Landau
level.
