  Systems of Y-junctions are interesting both from a fundamental viewpoint and
because of their potential use in nanoscale devices. These systems can be
studied numerically with the density matrix renormalization group(DMRG), but
existing algorithms are inefficient. Here, we introduce a much more efficient
DMRG algorithm for Y-junction systems. As an example of the use of this method,
we study $S=1/2$ bound states in Heisenberg S=1 junctions with two geometries,
one where the junction consists of a single site, and the other where it
consists of a triangle of three sites.
