Exotic Versus Conventional Scaling and Universality in a Disordered Bilayer Quantum Heisenberg Antiferromagnet

We present Monte Carlo simulations of a two-dimensional bilayer quantum Heisenberg antiferromagnet with random dimer dilution. In contrast with exotic scaling scenarios found in other random quantum systems, the quantum phase transition in this system is characterized by a finite-disorder fixed point with power-law scaling. After accounting for corrections to scaling, with a leading irrelevant exponent of $\omega \approx 0.48$, we find universal critical exponents $z=1.310(6)$ and $\nu =1.16(3)$. We discuss the consequences of these findings and suggest new experiments.

Figure 1

Phase diagram [20] of the diluted bilayer Heisenberg antiferromagnet, as function of $J_{\perp }/J_{\parallel }$ and dilution $p$. The dashed line is the percolation threshold, the open dot is the multicritical point of Refs. 19, 20. The arrow indicates the QPT studied here. Inset: the model: quantum spins (arrows) reside on the two parallel square lattices. The spins in each plane interact with the coupling strength $J_{\parallel }$. Interplane coupling is $J_{\perp }$. Dilution is done by removing dimers.

Figure 2

Upper panel: Binder ratio $g_{av}$ as a function of $L_{\tau }$ for various $L$ ($p=\frac{1}{5}$). Lower panel: Power-law scaling plot $g_{av}/g_{av}^{\mathrm{m}\mathrm{a}\mathrm{x}}$ vs $L_{\tau }/L_{\tau }^{\mathrm{m}\mathrm{a}\mathrm{x}}$. Inset: Activated scaling plot $g_{av}/g_{av}^{\mathrm{m}\mathrm{a}\mathrm{x}}$ vs $y=\log (L_{\tau })/\log (L_{\tau }^{\mathrm{m}\mathrm{a}\mathrm{x}})$.

Figure 3

$L_{\tau }^{\mathrm{m}\mathrm{a}\mathrm{x}}/L$ vs $L$ for four disorder concentrations $p=\frac{1}{8}$, $\frac{1}{5}$, $\frac{2}{7}$, and $\frac{1}{3}$. Solid lines: fit to $L_{\tau }^{\mathrm{m}\mathrm{a}\mathrm{x}}=a{L}^z(1+b{L}^{-{\omega }_1})$ with $z=1.310(6)$ and ${\omega }_1=0.48(3)$.

Figure 4

Scaling plot of $g_{av}$ vs $(T-T_c)x_L$ for $p=0.2$. $x_L$ is the factor necessary to scale the data onto a master curve.

Figure 5

Scaling factor vs $L$ for four disorder concentrations $p=\frac{1}{8}$, $\frac{1}{5}$, $\frac{2}{7}$, and $\frac{1}{3}$. Solid lines: fit to $x_L=c{L}^{1/\nu }(1+d{L}^{-{\omega }_2})$ with $\nu =1.16(3)$ and ${\omega }_2=0.5(1)$.