I'm running a spin chain simulations for tests, open boundary conditions. The dimension of local Hilbert space is N. On the "backwards" part of the sweep, it seems like the algorithm is keeping many more states than physically (or by Schmidt decomposition theorem, allowed).

For instance, for N=3, it claims to keep 69 states on bond (1,2), whereas the left part of the Hilbert space, consisting of a single spin, has dimension 3 only. This does not happen on the "forward" part of the sweep, where 3 states are kept.

Is this departure from the optimal Schmidt number of states correct?

Is this perhaps the effect of the noise term?