The ground state phase of spin-1/2 J1-J2 antiferromagnetic Heisenberg model on square lattice around the maximally frustrated regime (J2 ∼ 0.5J1) 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 J2c1 = 0.572(5)J1 and critical exponents ν = 0.50(8), ηs = 0.28(6). In the range of 0.572 < J2/J1 < 0.6 we find a paramagnetic ground state with exponentially decaying spin-spin correlation. Up to 24 × 24 system size, we observe power law decaying dimer-dimer and plaquette-plaquette correlations with an anomalous plaquette scaling exponent ηp = 0.24(1) and an anomalous columnar scaling exponent ηc = 0.28(1) at J2/J1 = 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 VBS order with very small amplitude might develop in the thermodynamic limit. Thus, the numerical results strongly indicate a deconfined quantum critical point (DQCP) at J2c1 . Remarkably, all the observed critical exponents are consistent with the J − Q model.

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**Reference: **L. Wang, Z.-C. Gu, F. Verstraeten and X.-G. Wen, *“Tensor-product state approach to spin-1/2 square J1-J2 antiferromagnetic Heisenberg model: Evidence for deconfined quantum criticality”*, Physical Review B (2016)

**Fig. left: **A benchmark of ground state energy with the SU(2) symmetric DMRG results on tori and the VMC calculation with one Lanczos projection step on tori at J2 = 0.5, 0.55, where Dc is the Schmidt number kept in our VMC-tensor renormalization algorithm.

**Fig. right: **The finite size scaling function of C(L/2,L/2), from where we determine the critical point J2c1, and spin-correlation length exponent ν and the anomalous spin correlation exponent ηs.

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**Fig. right: **The modified dimer-dimer correlation Cdx∗ (r, r) (a) and plaquette-plaquette correlation Cplq∗ (r, r) (b) as a function of separation r at J2 = 0.6 in log-log plots. (c) The valence bond solid order parameters S2col and S2plq at J2 = 0.6 as functions of 1/L in log-log plot. The power law decay behaviors are captured by decay exponents 1 + ηp = 1.24(1) and 1 + ηc = 1.28(1) for the plaquette and columnar VBS order respectively.**Fig. left:** (a) The largest distance spin-spin correlation as a function of J2 at L = 8, 12, 16, 24. The same correlations C(L/2,L/2) presented against 1/L in a regular plot (b) and in a log-log plot (c) for various J2.