  We investigate transport of spinless fermions through a single site dot
junction of M one-dimensional quantum wires. The semi-infinite wires are
described by a tight-binding model. Each wire consists of two parts: the
non-interacting leads and a region of finite extent in which the fermions
interact via a nearest-neighbor interaction. The functional renormalization
group method is used to determine the flow of the linear conductance as a
function of a low-energy cutoff for a wide range of parameters. Several fixed
points are identified and their stability is analyzed. We determine the scaling
exponents governing the low-energy physics close to the fixed points. Some of
our results can already be derived using the non-self-consistent Hartree-Fock
approximation.
