We consider unitary analogs of dβdimensional Anderson models on l2(Zd)
defined by the product UΟβ=DΟβS where S is a deterministic
unitary and DΟβ is a diagonal matrix of i.i.d. random phases. The
operator S is an absolutely continuous band matrix which depends on
parameters controlling the size of its off-diagonal elements. We adapt the
method of Aizenman-Molchanov to get exponential estimates on fractional moments
of the matrix elements of UΟβ(UΟββz)β1, provided the
distribution of phases is absolutely continuous and the parameters correspond
to small off-diagonal elements of S. Such estimates imply almost sure
localization for UΟβ