Can the bond dimension of the singular value tensor be 0 after performing SVD? If so, under what circumstances can this happen? Currently, I am performing SVD on a tensor with multiple legs, including quantum numbers, and this issue arises.
That will happen if the matrix/tensor you are SVDing is zero (i.e. has zero norm). For a QN tensor, that could happen if there are no allowed QN sectors for the combination of sectors on the indices of the tensor.