Valence bond - fast implementation (2)

Question

Hi everyone,

I actually have a follow-up question about this:
https://itensor.org/support/1920/valence-bond-states-fast-implementation

So I have created a state like this. It is basically a product of 2-site states, which can either be nearest neighbors or arbitrary sites i,j (for arbitrary sites I need to change the site indices after I generate a nearest-neighbor product state, we discussed that in the previous thread).

My question is, after I have created an MPS state that represents the equation above, how can I change the coefficients u and d, without needing to generate the state from scratch? Is there a way?

Thank you very much in advance.

Comments

Hi, so I think I know the answer but I might be missing some aspect of what you are doing. Do you think it would work to:
(1) devise a two-site unitary gate which rotates the state of the two entangled sites back to being a trivial product state
(2) apply this gate to the two sites i,j whose state you want to change
(3) reapply a new gate to sites i,j which re-makes the entangled state but now with a different u and d?

Let me know if that sounds like it would work -

Miles

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Thank you very much for your reply.

This can probably work, but what I was betting on was whether there is a way to change the tensors directly. My understanding, however, is that for complicated sites (that are not nearest neighbors), that is non trivial.

Anyway, I will give it a try and see how much faster it becomes. Thank you very much!

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In general you would need to change not only the tensors at i and j but also every tensor in between, though you are probably aware of that. So the approach with using swaps to implement non-nearest neighbor gates is essentially the most efficient thing you can do.

Answer 1

(See discussion in above comments)