A tensor product state approach to spin-1/2 square J1-J2 antiferromagnetic Heisenberg model: evidence for deconfined quantum criticality

Abstract

The ground state phase diagram 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 a recently proposed novel numerical method - 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. At the largest bond dimension available D = 9 and through finite size scaling of the magnetization order near the transition point, we accurately determine the critical point Jc=0.5321(2)J1 and the critical exponent beta = 0.499(3). In the range of 0.5321<J2/J1<=0.6 we find a paramagnetic ground state without any static valence bond solid (VBS) order, supported by an exponentially decaying spin-spin correlation while a power law decaying dimer-dimer correlation, which suggests 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 at long wave length. Remarkably, by fitting a universal scaling function for the spin-spin correlation with fixed Jc find the critical exponents nu=0.68(3) and eta=0.34(3), which is in very good agreement to the observed critical exponents for deconfined quantum critical point (DQCP) in other systems. Thus, our numerical results strongly suggest a Landau forbidden phase transition from Neel order to VBS order at Jc=0.5321(2)J1.