Enhance simple_update! for MPS in the Canonical form

[jofrevalles]

Summary

This PR refactors the simple_update! function so now it properly uses the $\Lambda$ tensors of an MPS in the Canonical form to evolve the state without the need of recanonizing it.

Additionally, we also added the kwarg of normalize in the canonize! function.

[jofrevalles]

@mofeing @starsfordummies Maybe we should put the renormalize kwarg in all truncate! functions (for all the Forms), right? Since we will lose norm every time we truncate.

[starsfordummies]

ok for me!

[jofrevalles]

@mofeing I refactored the normalize functions, so now we can do normalize! of an MPS in the Canonical form without recanonizing. We can also choose the bond at which it normalizes it.

[mofeing]

@mofeing I refactored the normalize functions, so now we can do normalize! of an MPS in the Canonical form without recanonizing. We can also choose the bond at which it normalizes it.

nice! so I understand that if you don't provide the bond, then it normalizes all of them right? mmm do you have a use case for normalizing just 1 bond?

[jofrevalles]

nice! so I understand that if you don't provide the bond, then it normalizes all of them right? mmm do you have a use case for normalizing just 1 bond?

So I did not implemented it like that but I will change it so it is like you said. Maybe a use case would be when you truncate, right? Since you only truncate a bond and thus you want to renormalize the only "perturbed" bond.

[jofrevalles]

I will do some more tests on evolve! this afternoon, for now let's keep this PR open. I think I can finish it today.

[mofeing]

So I did not implemented it like that but I will change it so it is like you said. Maybe a use case would be when you truncate, right? Since you only truncate a bond and thus you want to renormalize the only "perturbed" bond.

that could be a case. in general you would want such a method in the case that you want to normalize 1 $\Lambda$ and keep the rest of $\Lambda$s intact but I can't think of a real case where you would want that. if you want to normalize all the $\Lambda$s (or only one) calling normalize! on each $\Lambda$ shouldn't be costly because they're just vectors.

[jofrevalles]

Okay for me this is ready to merge @starsfordummies @mofeing . I found that, in order to normalize all $\Lambda$, you need to divide all of them by norm(mps)^(1/(L-1)).

[mofeing]

okay, but can you check these comments?
https://github.com/bsc-quantic/Tenet.jl/pull/255/files#r1850557758
https://github.com/bsc-quantic/Tenet.jl/pull/255/files#r1850558850

also, on normalize!(::Canonical), doesn't just calling normalize! individually on each $\lambda$ just work?

[codecov]

Codecov Report

Attention: Patch coverage is 0% with 47 lines in your changes missing coverage. Please review.

Project coverage is 0.04%. Comparing base (0ba1707) to head (3ffd4e0).
Report is 2 commits behind head on master.

Files with missing lines	Patch %	Lines
src/Ansatz.jl	0.00%	29 Missing ⚠️
src/MPS.jl	0.00%	17 Missing ⚠️
src/Quantum.jl	0.00%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #255       +/-   ##
==========================================
- Coverage   79.59%   0.04%   -79.55%     
==========================================
  Files          32      32               
  Lines        2068    2072        +4     
==========================================
- Hits         1646       1     -1645     
- Misses        422    2071     +1649     

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[jofrevalles]

Okay, this was complicated... @mofeing @starsfordummies I finally managed to make everything work. For me, this makes sense. At least now, I think tomorrow I will forget for sure... Let's try to write it here:
evolve! has a renormalize kwarg, that for NonCanonical or MixedCanonical passes through truncate. This can not be done for Canonical, since simple_update_2site!(::Canonical, ...) contracts the two-site wave-function, evolves by calling simple_update_2site!(::NonCanonical, ...), and the truncate is there, but we need to truncate after that, when in we recover the (pseudo)Canonical form, and then is when we have to normalize! the bond.