Can we tune how often we run `calc_convergence`?

[kshyatt]

For my GPU stuff, I'm finding this check is quite expensive because it calls a lot of SVD (which scales poorly there) -- could we make the checking interval something settable by the user?

[lkdvos]

Looking a bit more into this, I'm assuming this is in the CTMRG iterations right?
One thing I was wondering is if we could actually get away with just comparing the spectrum of the (half)-infinite environment instead, which we need for the projectors, eliminating these extra SVDs completely? I agree the scale might be slightly different, but I have a vague idea these should in some sense be equivalent?

Alternatively, there is also a way to compare spectra without computing the SVD through spectral moments or Schatten norms, but I have very little intuition about how well this gives a proper estimate. The main idea is that you can obtain $$\sum_i \sigma_i^k$$ by taking tr(A^k), so it might be sufficient to take the first couple of these and compare them. It does sound to me like that is mostly sensitive to the larger values, but it might also be worth a shot.

[Yue-Zhengyuan]

What if we use network_value to check CTMRG convergence, which only involves tensor contraction? We know it often happens that the corner SVD spectrum may alternate between two (or more) values instead of converging to one value (possibly due to spontaneously broken translation symmetry). But in such cases network_value remains stable has a smaller fluctuation. (See an example at #255 (comment)) Are there cases where network_value can be unreliable?

[leburgel]

I think I have the opposite concern with using network_value as the convergence criterion, namely that it might be too easy to converge. This would feel like using the energy convergence to assess the convergence of an optimization, we generally don't want to directly use the objective function for this.