Evidence for Deconfined Quantum Criticality in a Two-Dimensional Heisenberg Model with Four-Spin Interactions

Using ground-state projector quantum Monte Carlo simulations in the valence-bond basis, it is demonstrated that nonfrustrating four-spin interactions can destroy the Néel order of the two-dimensional $S=1/2$ Heisenberg antiferromagnet and drive it into a valence-bond solid (VBS) phase. Results for spin and dimer correlations are consistent with a single continuous transition, and all data exhibit finite-size scaling with a single set of exponents, $z=1$, $\nu =0.78\pm 0.03$, and $\eta =0.26\pm 0.03$. The unusually large $\eta$ and an emergent $U(1)$ symmetry, detected using VBS order parameter histograms, provide strong evidence for a deconfined quantum critical point.

Figure 1

Finite-size scaling of the squared spin ($M$) and dimer ($D$) order parameters at $J/Q=0$ and 0.1. The curves are cubic fits. Statistical errors are much smaller than the symbols.

Figure 2

Finite-size scaling of the singlet-triplet excitation gap multiplied by the system size $L$. The behavior at $J/Q=0.04$ corresponds to $z=1$.

Figure 3

Scaling with $\nu =0.78$ and $g_c=0.04$ of the correlation lengths (a) and the spin Binder ratio (b).

Figure 4

Long-distance spin and dimer correlations scaled using $\nu =0.78$, $\eta =0.26$, and $g_c=0.04$.

Figure 5

Histogram of the dimer order parameter for an $L=32$ system at $J/Q=0$. The ring shape demonstrates an emergent $U(1)$ symmetry, i.e., irrelevance of the $Z_4$ anisotropy of the VBS order parameter.