Fractal Quantum Phase Transitions: Critical Phenomena Beyond Renormalization

Abstract

We identify a quantum critical point with fractal symmetry whose effective theory eludes the renormalization group framework. We consider the Newman-Moore model with three-body interaction subjected to an external transverse field, which exhibits a Kramers-Wannier type self-duality and a fractal $Z_2$ symmetry with Ising charge conserved on a fractal subset of sites, i.e., on Sierpinski gaskets. Using large-scale quantum Monte Carlo simulations, we identify a continuous quantum phase transition between a phase with spontaneous fractal symmetry breaking and a paramagnetic phase. This phase transition is characterized by the emergence of a fractal scaling dimension $d=\ln (3)/\ln (2)$ at the quantum critical point, where the power-law exponent of the correlation function is related to the fractal dimension of the Sierpinski triangle. We develop a field theory to elucidate such quantum criticality and denote the fractal scaling as a subsequence of UV-IR mixing, where the low energy modes at the critical point are manipulated by short-wavelength physics due to the fractal symmetry.

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Cited by in corpus (7)

• The low-energy limit of some exotic lattice theories and UV/IR mixing
• Anomaly Inflow for Subsystem Symmetries
• Higher-Form Subsystem Symmetry Breaking: Subdimensional Criticality and Fracton Phase Transitions
• From Symmetries to Commutant Algebras in Standard Hamiltonians
• Building models of topological quantum criticality from pivot Hamiltonians
• Towards Non-Invertible Anomalies from Generalized Ising Models
• Emergent criticality in a constrained boson model