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.

DOI: 10.48550/arxiv.2101.01724

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U(1)

symmetry whose low energy modes contain a Bose surface along the

k_x,k_y

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 this finding by measuring the entanglement entropy, topological 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 fluctuation with peculiar UV-IR mixing.

Lln(L)

. Using the density matrix renormalization group method, we analyze the dipole stiffness together with the structure factor at the QCP, which provides strong evidence of a critical dipole liquid with a Bose surface, UV-IR mixing, and a dispersion relation $\ensuremath{\omega}={k}_{x}{k}_{y}.$

U(1)

symmetry and the breakdown of the area law entanglement entropy which exhibits a logarithmic enhancement:

L \ln(L)

. Using the density matrix renormalization group (DMRG) method, we analyze the dipole stiffness together with structure factor at the QCP which provide strong evidence of a critical dipole liquid with a Bose surface. These numerical signatures further support the fracton dynamics of the QCP, and suggest a new paradigm for 2D quantum criticality proximate to a topological phase.

z

link or a plaquette in the $x\text{\ensuremath{-}}y$ plane. The space of such fully packed tilings has an extensive degeneracy. This maps onto a fracton-type ``higher-rank electrostatics,'' which can exhibit a plaquette-dimer liquid and an ordered phase. We analyze this theory in detail, using height representations and T-duality to demonstrate that the concomitant phase transition occurs due to the proliferation of dipoles formed by defect pairs. The resultant critical theory can be considered as a fracton version of the Kosterlitz-Thouless transition. A significant new element is its UV-IR mixing, where the low-energy behavior of the liquid phase and the transition out of it is dominated by local (short-wavelength) fluctuations, rendering the critical phenomenon beyond the renormalization group paradigm.