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.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.

arXiv:2105.05851May 12, 202115 citations

Seeing quantum fractals

Physics TodayFeb 23, 20100 citations

Fractals and the Quantum Classical Boundary

Garnet N. Ord

Chaos Solitons & FractalsAug 1, 19997 citations

Multipartite entanglement, quantum coherence, and quantum criticality in triangular and Sierpiński fractal lattices

Jun-Qing Cheng, Jing‐Bo Xu

We investigate the quantum phase transitions of the transverse-field quantum Ising model on the triangular lattice and Sierpiński fractal lattices by employing the multipartite entanglement and quantum coherence along with the quantum renormalization group method. It is shown that the quantum criticalities of these high-dimensional models closely relate to the behaviors of the multipartite entanglement and quantum coherence. As the thermodynamic limit is approached, the first derivatives of the multipartite entanglement and quantum coherence exhibit singular behaviors, and the consistent finite-size scaling behaviors for each lattice are also obtained from the first derivatives. The multipartite entanglement and quantum coherence are demonstrated to be good indicators for detecting the quantum phase transitions in the triangular lattice and Sierpiński fractal lattices. Furthermore, the dimensions determine the relations between the critical exponents and the correlation length exponents for these lattices.We investigate the quantum phase transitions of the transverse-field quantum Ising model on the triangular lattice and Sierpiński fractal lattices by employing the multipartite entanglement and quantum coherence along with the quantum renormalization group method. It is shown that the quantum criticalities of these high-dimensional models closely relate to the behaviors of the multipartite entanglement and quantum coherence. As the thermodynamic limit is approached, the first derivatives of the multipartite entanglement and quantum coherence exhibit singular behaviors, and the consistent finite-size scaling behaviors for each lattice are also obtained from the first derivatives. The multipartite entanglement and quantum coherence are demonstrated to be good indicators for detecting the quantum phase transitions in the triangular lattice and Sierpiński fractal lattices. Furthermore, the dimensions determine the relations between the critical exponents and the correlation length exponents for these lattices.

arXiv:1802.03177Physical review. EJun 19, 201811 citations

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.