A lattice model for the SU(N) Neel-VBS quantum phase transition at large N

TL;DR

This paper studies the quantum phase transition between Ne9el and valence-bond-solid states in an SU(N) magnet model at large N, using quantum Monte Carlo simulations to support deconfined quantum-criticality theory.

Contribution

It generalizes the SU(2) quantum magnet model to arbitrary N and provides numerical evidence for the universality of the Ne9el-VBS transition at large N.

Findings

Both order parameters vanish at a single quantum-critical point.

Universal exponents approach 1/N expansion values for N up to 12.

Results support the deconfined quantum-criticality theory.

Abstract

We generalize the SU(N=2) $S=1/2$ square-lattice quantum magnet with nearest-neighbor antiferromagnetic coupling ($J_1$) and next-nearest-neighbor ferromagnetic coupling ($J_2$) to arbitrary $N$. For all $N>4$, the ground state has valence-bond-solid (VBS) order for $J_2=0$ and N\'eel order for $J_2/J_1\gg 1$, allowing us access to the transition between these types of states for large $N$. Using quantum Monte Carlo simulations, we show that both order parameters vanish at a single quantum-critical point, whose universal exponents for large enough $N$ (here up to N=12) approach the values obtained in a 1/N expansion of the non-compact CP$^{N-1}$ field theory. These results lend strong support to the deconfined quantum-criticality theory of the N\'eel--VBS transition.