A tensor product state approach to spin1/2 square J_1J_2
antiferromagnetic Heisenberg model: evidence for deconfined quantum
criticality
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by
Ling Wang, ZhengCheng Gu, Frank Verstraete, XiaoGang Wen
2011
Abstract
The ground state phase of spin1/2 J_1J_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 spinspin correlation. Up to 24× 24
system size, we observe power law decaying dimerdimer and plaquetteplaquette
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 JQ model.
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Stage
submitted
Date 20111214
Version
v1
Language
en
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1112.3331v1
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