  Localization by a broken particle-hole symmetry in a random system of
non-interacting quantum particles is studied on a $d$--dimensional lattice. Our
approach is based on a chiral symmetry argument and the corresponding invariant
measure, where the latter is described by a Grassmann functional integral.
Within a loop expansion we find for small loops diffusion in the case of
particle-hole symmetry. Breaking the particle-hole symmetry results in the
creation of random dimers, which suppress diffusion and lead to localization on
the scale $\sqrt{D/|\mu|}$, where $D$ is the effective diffusion coefficient at
particle-hole symmetry and $\mu$ is the parameter related to particle-hole
symmetry breaking.
