Percolation quantum phase transitions in diluted magnets

TL;DR

This paper investigates a new universality class for percolation quantum phase transitions in diluted magnets, highlighting how quantum fluctuations alter classical critical behavior and providing exact results in two dimensions.

Contribution

It introduces a complete scaling theory for the percolation quantum phase transition and connects it to experimental observations and disordered boson systems.

Findings

Critical exponents involving dynamical correlations differ from classical percolation.

In two dimensions, critical exponents can be determined exactly.

The theory is related to experiments in La$_{2}$Cu$_{1-p}$(Zn,Mg)$_{p}$O$_{4}$.

Abstract

We show that the interplay of geometric criticality and quantum fluctuations leads to a novel universality class for the percolation quantum phase transition in diluted magnets. All critical exponents involving dynamical correlations are different from the classical percolation values, but in two dimensions they can nonetheless be determined exactly. We develop a complete scaling theory of this transition, and we relate it to recent experiments in La$_{2}$Cu$_{1-p}$(Zn,Mg)$_{p}$O$_{4}$. Our results are also relevant for disordered interacting boson systems.