Belief propagation for purified iPEPO

[Yue-Zhengyuan]

This PR adds belief propagation for purified iPEPO (iPEPS with two physical legs). It is tested by gauge-fixing finite-temperature simple update results and checking that the expectation values are unaffected.

In addition, I feel we need to distinguish gauge_fix for states and for CTMRGEnv. So here I also renamed the CTMRG gauge fixing to env_gauge_fix, and exported gauge_fix.

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.

Files with missing lines	Coverage Δ
src/PEPSKit.jl	100.00% <ø> (ø)
src/algorithms/bp/gaugefix.jl	97.36% <100.00%> (ø)
...rithms/optimization/fixed_point_differentiation.jl	91.72% <ø> (ø)
src/environments/bp_environments.jl	87.75% <100.00%> (ø)
src/operators/infinitepepo.jl	76.85% <100.00%> (+0.43%)	⬆️

... and 3 files with indirect coverage changes

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[lkdvos]

Looks great, thanks!

I think my only remark is that I don't think we should really avoid using gauge_fix for the CTMRG environments, we can use dispatch to distinguish between the two and both use-cases really are of similar nature.
In principle we may at some point want to experiment with the different CTMRG environment gaugefixes, and introduces algorithm types for that too, so then these things look even more alike.

I don't feel too strongly about this and I'm happy to revisit that later if you feel like already merging this, or maybe someone else can give another opinion on the matter?

[Yue-Zhengyuan]

Another reason for the renaming is that I want to export gauge_fix for the state, but don't want to unwillingly export gauge_fix for the CTMRGEnv as a by-product. But anyway, I feel that the interface for both cases is subject to possibly big changes in the near future, so I can also definitely undo the renaming and not export any of them.

[lkdvos]

I have no issues with exporting them and possibly changing them in the near future. If people want to use this while it's not supported, they would still have to change their code if we make changes to this so in the end it doesn't really make such a big difference

[Yue-Zhengyuan]

OK then. I undid the renaming to make the diff smaller.