  Fracton topological order (FTO) is a new classification of correlated phases
in three spatial dimensions with topological ground state degeneracy (GSD)
scaling up with system size, and fractional excitations which are immobile or
have restricted mobility. With the topological origin of GSD, FTO is immune to
local perturbations, whereas a strong enough global external perturbation is
expected to break the order. The critical point of the topological transition
is however very challenging to identify. In this work, we propose to
characterize quantum phase transition of the type-I FTOs induced by external
terms and develop a theory to study analytically the critical point of the
transition. In particular, for the external perturbation term creating
lineon-type excitations, we predict a generic formula for the critical point of
the quantum phase transition, characterized by the breaking-down of GSD. This
theory applies to a board class of FTOs, including X-cube model, and for more
generic FTO models under perturbations creating two-dimensional (2D) or 3D
excitations, we predict the upper and lower limits of the critical point. Our
work makes a step in characterizing analytically the quantum phase transition
of generic fracton orders.
