Percolation Quantum Phase Transitions in Diluted Magnets

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 ${\mathrm{La}}_2{\mathrm{Cu}}_{1-p}(\mathrm{Zn},\mathrm{Mg}{)}_p{\mathrm{O}}_4$. Our results are also relevant for disordered interacting boson systems.

Figure 1

Schematic phase diagram of a diluted magnet with impurity concentration $p$, temperature $T$, and quantum fluctuation strength $g$ [30]. There is a quantum multicritical point (big dot) at $(p_c,g^{*})$. The zero temperature quantum phase transition across the dashed line is the topic of this Letter.

Figure 2

For $g<g^{*}$, a percolation cluster acts as a compact object. The spins are correlated in space but collectively fluctuate in imaginary time $\tau$.

Figure 3

Exponents $\gamma$, $\delta$, and $z$ as functions of $z_0$ in 2D. The limiting cases $z_0\to 0$ and $z_0\to 2$ are explained in the text.