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.
