VUMPS convergence issues

ITensor Julia Questions
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I am resurrecting this thread (and similar threads like this one) as I have been unable to get VUMPS to converge for some site type: tJ systems (both 1D and cylinders.) I have been doing QN off calculations to study doping, but I have similar convergence issues for QN on) . I have tried some of the simplest solutions, such as requesting errors of even 10^{-10} or 10^{-12} for low bond dimensions or attempting to bias the low-bond dimension states by adding explicit Weiss fields to the Hamiltonian. Bond dimensions above 500 or so still have exponentially slow timescales and do not converge. I have been resorting to finite DMRG for a project instead.

While this still may just be a “skill issue” (I’m not sure if my attempts have been finding good approximations to the MPS or just messing with fixing the MPS gauge), I’m asking the community if there is perhaps a better way to go forward. From the forums, there are several directions I’ve seen

  1. Attempt to debug the experimental finite to infinite code to take my finite DMRG results to VUMPS
  2. Attempt to add a “noise” term to VUMPS. Could you just add a small noise term to your MPO? If it’s more sophisticated, I would need a reference.
  3. Attempt to learn TEBD and do this before VUMPS. (I’m hesitant to do this because it seems too much of a stop-gap workaround, but it’s been suggested so frequently, perhaps this is best practice?)
  4. Attempt to extend the finite DMRG code to iDMRG. (I have read conflicting things about how similar VUMPS vs iDMRG results are and this would be the most serious undertaking)
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Hi Andrew,

I encountered the issue of slow convergence using VUMPS in exactly solvable anisotropic Kitaev model. Having already invested significant time in writing my own iDMRG code, I ultimately focused on getting it to work instead of pursuing the VUMPS method further. In the case of exactly solvable Kitaev model, I encountered convergence issues with both VUMPS and 2-site iDMRG. I resolved the issue by adding subspace expansion to the 2-site iDMRG (see DMRG3S), so I guess the convergence issue encountered in VUMPS can also be resolved by implementing subspace expansion of some sort. Yet another way is to add “noise” by perturbing the MPS as delineated here density matrix perturbation. See Matt’s comment in https://itensor.discourse.group/t/difficulty-with-simulating-a-specific-model-with-vumps-that-works-perfectly-fine-with-regular-dmrg/2027/4.

Best,
Xu

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Hi Xu,

Very insightful thank you! Have you thought about making your 2-site iDMRG code public or integrating with the iTensor suite? It’s probably the most requested feature on this forum and even if I were to write my own, it would be nice to have benchmarks.

If you were motivated, you could probably also publish it under Journal of Open Source Software , which is not that much harder than making a GitHub repo.

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Yeah I’ve been thinking about this as well. I am pretty occupied recently but I do plan to clear up my iDMRG code (it works well for my projects but is still not general and lacks several features) and post it out early next year.

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