A tensor product state approach to spin-1/2 square J_1-J_2
antiferromagnetic Heisenberg model: evidence for deconfined quantum
Ling Wang, Zheng-Cheng Gu, Frank Verstraete, Xiao-Gang Wen
The ground state phase of spin-1/2 J_1-J_2 antiferromagnetic Heisenberg
model on 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_2^c_1=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 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 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 VBS order with very small amplitude might develop in the thermodynamic limit.
Thus, our numerical results strongly indicate a deconfined quantum critical
point (DQCP) at J_2^c_1. Remarkably, all the observed critical exponents
are consistent with the J-Q model.
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