Protected percolation: a new universality class pertaining to heavily-doped quantum critical systems

TL;DR

This paper introduces a new universality class called protected percolation, modeled through large-scale simulations, which explains the unique critical behavior observed in heavily-doped quantum critical systems and challenges existing theoretical criteria.

Contribution

The study defines and characterizes a novel protected percolation universality class through extensive simulations, linking it to quantum critical phenomena.

Findings

Protected percolation forms a new universality class.

Critical exponents differ from standard percolation.

Violates the Harris criterion, explaining elusive quantum exponents.

Abstract

We present the results of computer simulations on a class of percolative systems that forms a new universality class. We show the results for the critical exponents for this new class, inferred from simulations of two- and three-dimensional lattices consisting of up to one billion lattice sites. These new percolative systems differ from standard percolative systems in that once a cluster breaks off the lattice spanning cluster, its sites become protected and cannot be removed. This situation closely mimics the situation in heavily-doped quantum critical systems where isolated magnetic clusters are protected from (further) Kondo screening. Our results indicate that protected percolation violates the Harris criterion, which yields a natural explanation as to why universal exponents for quantum phase transitions have been elusive.