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We propose an unconventional topological quantum phase transition connectinga higher-order topological insulator (HOTI) and a featureless Mott insulatorsharing the same symmetry patterns. We construct an effective theorydescription of the quantum critical point (QCP) by combining a bosonizationapproach and the coupled-stripe construction of 1D critical spin ladders. Thephase transition theory is characterized by a critical dipole liquid theorywith subsystem $U(1)$ symmetry whose low energy modes contain a Bose surfacealong the $k_x,k_y$ axis. Such a quantum critical point manifests fractondynamics and the breakdown of the area law entanglement entropy due to theexistence of a Bose surface. We numerically confirm our findings by measuringthe entanglement entropy, topological rank-2 Berry phase, and the staticstructure factor throughout the topological transition and compare it with ourprevious approach obtained from the percolation picture. A significant newelement of our phase transition theory is that the infrared~(IR) effectivetheory is controlled by short wave-length fluctuations with peculiar UV-IRmixing.

Fractonic critical point proximate to a higher-order topological insulator: How does UV blend with IR?