Deconfined-critical behavior of the VBS- and nematic-order parameters for the spatially anisotropic S=1-spin model

The phase transition between the valence-bond-solid (VBS) and nematic phases, the so-called deconfined criticality, was investigated for the quantum S=1-spin model on the spatially anisotropic triangular lattice with the biquadratic interaction by means of the numerical diagonalization method. We calculated both VBS- and nematic-order parameters, aiming to clarify the nature of this transition from complementary viewpoints. Simulating the clusters with N≤20 spins, we estimate the correlation-length critical exponent as ν=0.95(14). We also calculated Fisher’s exponent (anomalous dimension) for each order parameter.