Fractonic critical point proximate to a higher-order topological insulator: A Coupled wire approach

Abstract

We propose an unconventional topological quantum phase transition between a higher-order topological insulator (HOTI) and a featureless Mott insulator, both sharing the same symmetry patterns. Our approach constructs an effective theory for the quantum critical point (QCP) by combining a bosonization technique with the coupled-stripe construction of 1D critical spin ladders. This phase transition is characterized by a critical dipole liquid theory with subsystem $U$(1) symmetry, where the low-energy modes contain a Bose surface along the $k\text{\_}x,k\text{\_}y$ axis. This quantum critical point exhibits fracton dynamics and a breakdown of the area law for entanglement entropy, attributed to the presence of the Bose surface. We numerically validate our findings by measuring the entanglement entropy, topological rank-2 Berry phase, and static structure factor throughout the topological transition, comparing these results with our previous approach derived from the percolation picture. A significant new aspect of our phase transition theory is that the infrared (IR) effective theory is governed by short-wavelength fluctuations, demonstrating a unique UV-IR mixing.