  We introduce a two-dimensional active nematic with quenched disorder. We
write the coarse-grained hydrodynamic equations of motion for slow variables,
viz. density, and orientation. Disorder strength is tuned from zero to large
values. Results from the numerical solution of equations of motion as well as
the calculation of two-point orientation correlation function using linear
approximation show that the ordered steady-state follows a disorder-dependent
crossover from quasi long-range order (QLRO) to short-range order (SRO). Such
crossover is due to the pinning of +1/2 and -1/2 topological defects in the
presence of finite disorder, which breaks the system in uncorrelated domains.
Finite disorder slows the dynamics of +1/2 defect, and it leads to slower
growth dynamics. The two-point correlation functions for the density and
orientation fields show good dynamic scaling but no static scaling for the
different disorder strengths. Our findings can motivate experimentalists to
verify the results and find applications in living and artificial apolar
systems in the presence of a quenched disorder.
