Complex critical exponents for percolation transitions in Josephson-junction arrays, antiferromagnets, and interacting bosons

TL;DR

This paper reveals how topological Berry phases influence the critical behavior of quantum systems at percolation transitions, leading to unconventional phenomena like complex exponents and fractal spectra.

Contribution

It uncovers the impact of Berry phases on quantum percolation transitions, showing emergence of non-traditional critical phenomena in various systems.

Findings

Critical behavior is affected by Berry phase $2\pi ho$.

Low-energy excitations are spinless fermions with fractal spectra.

Emergence of complex critical exponents and log-periodic oscillations.

Abstract

We show that the critical behavior of quantum systems undergoing a percolation transition is dramatically affected by their topological Berry phase $2\pi\rho$. For irrational $\rho$, we demonstrate that the low-energy excitations of diluted Josephson-junctions arrays, quantum antiferromagnets, and interacting bosons are spinless fermions with fractal spectrum. As a result, critical properties not captured by the usual Ginzburg-Landau-Wilson description of phase transitions emerge, such as complex critical exponents, log-periodic oscillations and dynamically broken scale-invariance.