Néel-VBS phase boundary of the extended J ₁-J ₂ model with biquadratic interaction

The J ₁-J ₂ model with the biquadratic (plaquette-four-spin) interaction was simulated with the numerical diagonalization method. Some limiting cases of this model have been investigated thoroughly. Taking advantage of the extended parameter space, we survey the phase boundary separating the Néel and valence-bond-solid phases. According to the deconfined-criticality scenario, the singularity of this phase boundary is continuous, accompanied with unconventional critical indices. Diagonalizing the finite-size cluster with N≤36 spins, we observe a signature of continuous phase transition. Our tentative estimate for the correlation-length critical exponent is ν=1.1(3). In order to elucidate a nonlocal character of criticality, we evaluated the Roomany-Wyld β function around the critical point.