Implement full-infinite projector algorithm

[pbrehmer]

This PR will implement the full-infinite projector algorithm which SVDs the full 4x4 CTMRG environment, as suggested in #93.

To do this we will need to break up the expand/projectors/renormalize pattern we currently use to implement the CTMRG routine.

[codecov]

Codecov Report

Attention: Patch coverage is 88.00000% with 30 lines in your changes missing coverage. Please review.

Files with missing lines	Patch %	Lines
src/algorithms/ctmrg/sparse_environments.jl	0.00%	10 Missing ⚠️
src/utility/util.jl	50.00%	9 Missing ⚠️
src/algorithms/contractions/ctmrg_contractions.jl	60.00%	4 Missing ⚠️
src/algorithms/ctmrg/ctmrg.jl	90.47%	2 Missing ⚠️
src/algorithms/ctmrg/projectors.jl	94.87%	2 Missing ⚠️
src/algorithms/ctmrg/sequential.jl	98.27%	1 Missing ⚠️
src/algorithms/ctmrg/simultaneous.jl	98.50%	1 Missing ⚠️
src/environments/ctmrg_environments.jl	91.66%	1 Missing ⚠️

Files with missing lines	Coverage Δ
src/PEPSKit.jl	87.50% <ø> (ø)
src/algorithms/ctmrg/gaugefix.jl	98.00% <ø> (+2.95%)	⬆️
src/algorithms/peps_opt.jl	94.59% <100.00%> (-0.05%)	⬇️
src/algorithms/ctmrg/sequential.jl	98.27% <98.27%> (ø)
src/algorithms/ctmrg/simultaneous.jl	98.50% <98.50%> (ø)
src/environments/ctmrg_environments.jl	62.72% <91.66%> (+0.22%)	⬆️
src/algorithms/ctmrg/ctmrg.jl	93.75% <90.47%> (-0.30%)	⬇️
src/algorithms/ctmrg/projectors.jl	94.87% <94.87%> (ø)
src/algorithms/contractions/ctmrg_contractions.jl	70.37% <60.00%> (+1.13%)	⬆️
src/utility/util.jl	52.12% <50.00%> (+0.36%)	⬆️
... and 1 more

[pbrehmer]

This should almost be finished. CTMRG is now refactored with both HalfInfiniteProjector and FullInfiniteProjector running, at least in the forward pass. Somehow FullInfiniteProjector does not yet differentiate but I'll look at that on Monday. I have also added the new projector algorithm to the test suite.

@lkdvos Perhaps you could take a look at the refactoring whenever you have time? Thanks :-)

[lkdvos]

Overall, looks good!

I would say that I am a bit torn on using a flavor over a separate struct now, given that we are separating the algorithms in their own files and this results in having to come up with new names for functions that are doing the same thing, albeit via a different implementation. Maybe just something like this:

abstract type CTMRGAlgorithm end
struct SequentialCTMRG
  # fields....
end
struct SimultaneousCTMRG
end

could also work, although that is of course the same as the type aliases we had before. I like this slightly better since it doesn't require symbols, which are hard to constrain/remember the exact form of.

The projector code looks good, I think I would separate it into its own file, since it's now a substantial amount of code.

The remark about the race conditions is probably not super urgent, just wanted to at least mention it somewhere because I had noticed it and don't want to forget.

[pbrehmer]

So most things should work now. Again, the truncation space coordinates for the projectors really confused the hell out of me but FixedSpaceTruncation now works properly again.

Somehow FullInfiniteProjector still doesn't work for the :fixed mode differentiation (the others seem to work), so I'll have to see tomorrow where the problem lies.

[pbrehmer]

It should now differentiate also in the :fixed mode. It seems that the full-infinite projectors are just a bit unstable in general when it comes to differentiation (I think this is known?), so this leaves some room for experimentation. But from the implementation side this should be good to go, I hope.

I also updated the gauge-fixing test such that it hopefully is more stable now.

[lkdvos]

This looks good to me!

One remark might be that maybe we try to merge #97 first, since I don't want to make Yue have to rewrite his code (again). Could you have a look at that PR and tell us what you think?

[pbrehmer]

Yes, I'll take a look and then we can merge #97 first!

[Yue-Zhengyuan]

@pbrehmer Thanks for the great work! I'll adapt my code with the latest changes and open a PR on full update soon.