Could someone please help me with two questions about DMRG calculations for one-dimensional spin chain systems—using the built-in DMRG functions of ITensors and ITensorMPS?
First, for spin-1/2 systems, setting the max dimension to 1000 gives very accurate results. For systems with higher spins (e.g., 3/2, 5/2, etc.), what order of magnitude is roughly suitable for the max dimension setting?
Second, what is the approximate relationship between the max dimension setting and its impact on computation time?
Hi Lee,
As you may know, the maxdim parameter controls the bond dimension of an MPS, which sets a cap on the maximum entanglement S that an MPS can have (S \leq \log \chi where \chi is the bond dimension). It’s important to conjecture whether changing the spin size affects the bond dimension and entanglement, but how much it does is a highly problem-dependent statement. That is, one can imagine some Hamiltonians where going to higher spin makes the entanglement go down and others where it goes up. So you will need to just try with larger spins and see.
A good thing you can do is leave the maximum bond dimension (maxdim) high ,like at 1000, and then just raise the cutoff parameter to a value like 1E-4 or even 1E-3. This will set the accuracy at which DMRG will stop raising the bond dimension, so it will make the bond dimension typically come down a lot, while still guaranteeing (assuming DMRG is converged) that you will get an accuracy near the provided cutoff. This way you can do a fast calculation that is reasonably accurate, then gradually lower the cutoff to explore how quickly the bond dimension grows without doing a more common (and less advisable) thing which is to start right away with a tiny cutoff and then have a large bond dimension and very slow calculation.
Finally, the relationship of bond dimension and computation time is that computation time scales like \chi^3 where \chi is the typical (e.g. maximum over all the bonds) bond dimension of the MPS. Note that this is different from the maxdim value you provide, which just sets a hard upper limit on the bond dimension. Unless the cutoff you provide is very small or zero, the actual bond dimension of your MPS can often be well below the maxdim value you set.