  The honeycomb antiferromagnet under a triaxial strain is studied using the
quantum Monte Carlo simulation. The strain dimerizes the exchange couplings
near the corners, thus destructs the antiferromagnetic order therein. The
antiferromagnetic region is continuously reduced by the strain. For the same
strain strength, the exact numerical results give a much smaller
antiferromagnetic region than the linear spin-wave theory. We then study the
strained $XY$ antiferromagnet, where the magnon pseudo-magnetic field behaves
quite differently. The $0$th Landau level appears in the middle of the
spectrum, and the quantized energies above (below) it are proportional to
$n^{\frac{1}{3}} (n^{\frac{2}{3}})$, which is in great contrast to the
equally-spaced ones in the Heisenberg case. Besides, we find the
antiferromagnetic order of the $XY$ model is much more robust to the
dimerization than the Heisenberg one. The local susceptibility of the
Heisenberg case is extracted by the numerical analytical continuation, and no
sign of the pseudo-Landau levels is resolved. It is still not sure whether the
result is due to the intrinsic problem of the numerical analytical
continuation. Thus the existence of the magnon pseudo-Landau levels in the
spin-$\frac{1}{2}$ strained Heisenberg Hamiltonian remains an open question.
Our results are closely related to the two-dimensional van der Waals quantum
antiferromagnets and may be realized experimentally.
