Remove InfiniteWeightPEPS and mirror_antidiag

[Yue-Zhengyuan]

This PR is an overhaul of simple update, which removes InfiniteWeightPEPS and mirror_antidiag. The related tests and examples are updated accordingly. I apologize for not planning carefully before and introducing them in the first place.

• Simple update now works with InfinitePEPS and SUWeight. When a wpeps::InfiniteWeightPEPS was needed before, it is now replaced by peps::InfinitePEPS, env::SUWeight. The tensors in the InfinitePEPS correspond to InfiniteWeightPEPS.vertices with square root of bond weights always absorbed. Then InfiniteWeightPEPS is no longer useful, and we can get rid of its weird behaviors under lattice rotations.

• env::SUWeight is regarded as the environment for simple update, and hence the file defining it is moved to "environments/suweight.jl". Sometimes when CTMRG is also involved, the variable name is wts::SUWeight, with env reserved for CTMRGEnv.

• Axis order of SUWeight is no longer always (west, east) and (south, north), depending on the "dual-ness" of the Espaces and Nspaces of the PEPS. E.g. for x-weights, it is either 1 ← x ← 2 or 2 → x → 1. This makes logic in absorb_weight simpler.

• I added a _su_ybond! to directly update vertical bonds for the 2-site SU, without the need to mirror or rotate the PEPS. Hence mirror_antidiag is no longer needed and removed.

• I added some tricks in the half-filling Hubbard model SU example to improve convergence of SU and CTMRG (initialize with a small D = 4, then ramp up to a large D = 12, and finally go back to D = 8).

Things deliberately left for future PRs

• Rename su_iter, simpleupdate to timestep! and time_evolve to match MPSKit.
• Remember normalization used in each SU iteration. (I hope someone with a concrete use case can do it instead of myself.)

[Yue-Zhengyuan]

I have only updated the source files of the examples. We can regenerate the docs after we decide to merge this PR.

[codecov]

Codecov Report

❌ Patch coverage is 90.10417% with 19 lines in your changes missing coverage. Please review.

Files with missing lines	Patch %	Lines
src/environments/suweight.jl	82.69%	18 Missing ⚠️
src/algorithms/time_evolution/evoltools.jl	87.50%	1 Missing ⚠️

Files with missing lines	Coverage Δ
src/PEPSKit.jl	100.00% <ø> (ø)
src/algorithms/time_evolution/simpleupdate.jl	100.00% <100.00%> (ø)
src/algorithms/time_evolution/simpleupdate3site.jl	100.00% <100.00%> (ø)
src/algorithms/truncation/truncationschemes.jl	75.00% <ø> (+2.27%)	⬆️
src/networks/tensors.jl	75.00% <ø> (-1.00%)	⬇️
src/operators/localoperator.jl	86.40% <ø> (-0.87%)	⬇️
src/utility/util.jl	58.47% <100.00%> (ø)
src/algorithms/time_evolution/evoltools.jl	97.14% <87.50%> (+1.55%)	⬆️
src/environments/suweight.jl	82.69% <82.69%> (ø)

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[lkdvos]

Looks like an overall improvement, I like this.
I will try and make some more time to go over this, are you okay with me also pushing some small changes to this branch?

As a sidenote, this is definitely a breaking change, so shall I try and register a new patch version before we try to merge this?

[Yue-Zhengyuan]

@lkdvos Sure, please go ahead to make necessary changes.

We can register v0.6.1 for the current main branch. After this SU overhaul we may go to v0.7.

[lkdvos]

Left some small remarks, otherwise I'm happy to merge this!

[Yue-Zhengyuan]

Reminder: We need to regenerate the docs before merging.

[Yue-Zhengyuan]

I find some issues when regenerating the docs.