  Topological defects are a fossil relic of early Universe phase transitions,
with cosmic strings being the best motivated example. While in most cases one
studies Nambu-Goto or Abelian-Higgs strings, one also expects that
cosmologically realistic strings should have additional degrees of freedom in
their worldsheets, one specific example being superstrings from Type IIB
superstring theory. Here we continue the scientific exploitation of our
recently developed multi-GPU field theory cosmic strings code to study the
evolution of U(1)$\times$U(1) multitension networks, which are a numerically
convenient proxy: these contain two lowest-tension strings networks able to
interact and form bound states, providing a convenient first approximation to
the behaviour expected from cosmic superstrings. (...) We rely on the largest
field theory simulations of this model so far, specifically $4096^3$, $\Delta x
= 0.5$ boxes. We present robust evidence of scaling for the lightest strings,
measured through a complete and self-consistent set of correlation length and
velocity diagnostics. We also find a linearly growing average length of the
bound state segments, consistent with a scaling behaviour. (In previously
reported lower-resolution simulations, such behaviour had only been identified
with carefully engineered initial conditions, rich in those segments.) Finally,
while we see no evidence of a large population of bound states forming at early
stages of the network evolution, we do present tentative evidence for an
asymptotic constant value of the fraction of bound states, with this value
being different in the radiation and the matter eras. Our work demonstrates
that our GPU-accelerated field theory code can by successfully extended beyond
the simple Abelian-Higgs approximation, and enables future detailed studies of
realistic string networks and of their observational signatures.
