[Yue-Zhengyuan]

Adds gauge_transform for iPEPS, iPEPO, and CTMRGEnv, with separate VirtualGaugeTransform and CTMRGEnvGaugeTransform types for virtual bonds and environment boundary legs. Both support non-unitary matrices and inversion through inv.

Gauge fixing of CTMRG environment is refactored to use the general machinery of CTMRGEnvGaugeTransform.

Tests verify contraction invariance for PEPS, independent PEPO layers, and stacked networks.

[codecov]

Codecov Report

❌ Patch coverage is 90.06211% with 16 lines in your changes missing coverage. Please review.

Files with missing lines	Patch %	Lines
src/networks/gaugetransforms.jl	83.33%	11 Missing ⚠️
src/operators/infinitepepo.jl	60.00%	4 Missing ⚠️
src/algorithms/ctmrg/gaugetrans.jl	98.11%	1 Missing ⚠️

Files with missing lines	Coverage Δ
src/PEPSKit.jl	100.00% <ø> (ø)
src/algorithms/bp/gaugefix.jl	96.42% <100.00%> (+0.08%)	⬆️
src/algorithms/ctmrg/gaugefix.jl	95.14% <100.00%> (-0.54%)	⬇️
...lgorithms/optimization/implicit_differentiation.jl	91.56% <100.00%> (ø)
src/states/infinitepeps.jl	69.35% <100.00%> (+2.40%)	⬆️
src/algorithms/ctmrg/gaugetrans.jl	98.11% <98.11%> (ø)
src/operators/infinitepepo.jl	82.94% <60.00%> (+3.95%)	⬆️
src/networks/gaugetransforms.jl	83.33% <83.33%> (ø)

... and 2 files with indirect coverage changes

🚀 New features to boost your workflow:

• ❄️ Test Analytics: Detect flaky tests, report on failures, and find test suite problems.

[Yue-Zhengyuan]

Of course, there are some immediate generalizations to handle gauge freedoms in InfiniteSquareNetwork and its CTMRGEnv. But they'd better be added when someone encounters them in concrete applications. For now the only usage in my mind is BP gauge fixing for iPEPS norm network; after the fixing it is natural to transform its CTMRGEnv accordingly.

[leburgel]

I think this would be really great to have. Looking at this though, I'm wondering if it might be good to wrap the gauge matrices XXinv into a dedicated struct with properly documented indexing rules (basically just the diagrams you showed here). I think that might be a good reusable starting point for representing gauge transformations, even for more involved cases of different square networks. What do you think?

[kshyatt]

Sorry if I missed this but this does this also test with the new C4vCTRMGEnv? Not that I expect it to break but might be nice to be sure.

[Yue-Zhengyuan]

Gauge fixing for C4vCTMRGEnv is already tested in ctmrg_gaugefix_c4v of test/testsuite/ctmrg/gaugefix.jl. I didn't change the test function except one more @inferred check.

[kshyatt]

So I did miss it 😅 thanks!

[Yue-Zhengyuan]

A big source of type stability problem is rotation of unitary gauge transformations in an iPEPS. On each bond, the inverse gauge matrix is obtained as lazy AdjointTensorMaps. After a 90-degree rotation, as the bond direction changes, the AdjointTensorMaps will mix with TensorMaps.

Current solution: just remove definition of the rotation functions.