  We propose an unconventional topological quantum phase transition connecting
a higher-order topological insulator (HOTI) and a featureless Mott insulator
sharing the same symmetry patterns. We construct an effective theory
description of the quantum critical point (QCP) by combining a bosonization
approach and the coupled-stripe construction of 1D critical spin ladders. The
phase transition theory is characterized by a critical dipole liquid theory
with subsystem $U(1)$ symmetry whose low energy modes contain a Bose surface
along the $k_x,k_y$ axis. Such a quantum critical point manifests fracton
dynamics and the breakdown of the area law entanglement entropy due to the
existence of a Bose surface. We numerically confirm our findings by measuring
the entanglement entropy, topological rank-2 Berry phase, and the static
structure factor throughout the topological transition and compare it with our
previous approach obtained from the percolation picture. A significant new
element of our phase transition theory is that the infrared~(IR) effective
theory is controlled by short wave-length fluctuations with peculiar UV-IR
mixing.
