Tensor-product state approach to spin-1/2 square J_1−J_2 antiferromagnetic Heisenberg model: Evidence for deconfined quantum criticality

The ground state phase of a spin-1/2 J_1−J_2 antiferromagnetic Heisenberg model on a square lattice around the maximally frustrated regime (J_2∼0.5J_1) has been debated for decades. Here we study this model using the cluster update algorithm for tensor-product states (TPSs). The ground state energies at finite sizes and in the thermodynamic limit (with finite size scaling) are in good agreement with exact diagonalization study. Through finite size scaling of the spin correlation function, we find the critical point J^(c1)_2 = 0.572(5)J_1 and critical exponents ν = 0.50(8), η_s = 0.28(6). In the range of 0.572 < J_2/J_1 ≤ 0.6 we find a paramagnetic ground state with an exponentially decaying spin-spin correlation. Up to a 24×24 system size, we observe power law decaying dimer-dimer and plaquette-plaquette correlations with an anomalous plaquette scaling exponent η_p = 0.24(1) and an anomalous columnar scaling exponent η_c = 0.28(1) at J_2/J_1 = 0.6. These results are consistent with a potential gapless U(1) spin-liquid phase. However, since the U(1) spin liquid is unstable due to the instanton effect, a valence bond solid order with very small amplitude might develop in the thermodynamic limit. Thus, our numerical results strongly indicate a deconfined quantum critical point at J^(c1)_2. Remarkably, all the observed critical exponents are consistent with the J−Q model.