We investigate charge ordering in the Holstein model in the presence of anisotropic hopping, $t_x, t_y=1-delta, 1 + delta$, as a model of the effect of strain on charge density wave (CDW) materials. Using Quantum Monte Carlo simulations, we show that the CDW transition temperature is relatively insensitive to moderate anisotropy $delta lesssim 0.3$, but begins to decrease more rapidly at $delta gtrsim 0.4$. However, the density correlations, as well as the kinetic energies parallel and perpendicular to the compressional axis, change significantly for moderate $delta$. Accompanying mean-field theory calculations show a similar qualitative structure, with the transition temperature relatively constant at small $delta$ and a more rapid decrease for larger strains. We also obtain the density of states $N(omega)$, which provides clear signal of the charge ordering transition at large strain, where finite size scaling of the charge structure factor is extremely difficult because of the small value of the order parameter.
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