For Heisenberg chain, if I work in bond dimension 100, then the expansion term due to $H$ is a tensor of (2, 100, 5x100) dimension, which is not much. But for each projector, the same would be a tensor of (2, 100, 100x100), which is too large, and will grow ballistically with bond dimension. I just tried with this, but ram consumption is too high and the code is slow. Is there any other workaround to do it that you know? I didn't find any 'sparse' way do it, that does not involve any tensor product of bond indices involved in the projector.