Add Neighborhood Tensor Update (aka Cluster Update)

[Yue-Zhengyuan]

This PR adds the Neighborhood Tensor Update (NTU, arXiv 2107.06635) which is a variant of the Cluster Update (CU, arXiv 1110.4362 and arXiv 1311.6696).

When truncating a bond after applying a time evolution gate, the NTU uses some neighboring tensors as the bond environment, instead of using only a few bond weights (simple update) of the full iPEPS approximated by CTM (full update), "interpolating" between the two extremes. Currently the NN, NNN and NNN+ bond environments (see description in the YASTN package) are implemented.

Similar to the full update, the NTU often also needs to start from a good initialization (e.g. provided by simple update).

Differences from the NTU paper

• Bond weights are introduced in the iPEPS.
• The step of applying gate to the bond is made more efficient.
• Two ways of truncating the bond are implemented: ALSTruncation and FullEnvTruncation. The former is the traditional way to do it. The latter is proposed in arXiv 1801.05390 to truncate any internal bond in a network with closed loops. It seems that both have their own advantages.

To do

• Determine convergence criteria: with bond weights, the convergence can in principle be determined from the change of weights between two steps. But I observe that the energy can start to increase when the weight change is still decreasing.
• Compare with YASTN: the NTU was first implemented there. We should make sure that our implementation is as performant as (or even better than) theirs.
• Reduce code redundancy: some part of NTU code is very similar to SU.
• Polish docstrings.

[codecov]

Codecov Report

Attention: Patch coverage is 3.68764% with 444 lines in your changes missing coverage. Please review.

Files with missing lines	Patch %	Lines
src/algorithms/time_evolution/ntupdate.jl	0.00%	110 Missing ⚠️
.../algorithms/time_evolution/bondenv/optimize_als.jl	0.00%	75 Missing ⚠️
src/algorithms/time_evolution/bondenv/env_tools.jl	0.00%	70 Missing ⚠️
src/utility/fullenv_truncation.jl	0.00%	45 Missing ⚠️
src/algorithms/time_evolution/bondenv/env_ntu.jl	0.00%	34 Missing ⚠️
src/algorithms/time_evolution/bondenv/env_ctm.jl	0.00%	32 Missing ⚠️
src/states/infiniteweightpeps.jl	0.00%	18 Missing ⚠️
.../algorithms/time_evolution/bondenv/optimize_fet.jl	0.00%	16 Missing ⚠️
src/states/infinitepeps.jl	42.85%	16 Missing ⚠️
src/algorithms/time_evolution/simpleupdate.jl	0.00%	15 Missing ⚠️
... and 3 more

Files with missing lines	Coverage Δ
src/PEPSKit.jl	87.50% <ø> (ø)
src/algorithms/ctmrg/sequential.jl	98.36% <100.00%> (+0.08%)	⬆️
...rc/algorithms/time_evolution/bondenv/env_approx.jl	0.00% <0.00%> (ø)
src/utility/util.jl	51.54% <0.00%> (-1.09%)	⬇️
src/algorithms/time_evolution/evoltools.jl	0.00% <0.00%> (ø)
src/algorithms/time_evolution/simpleupdate.jl	0.00% <0.00%> (-87.92%)	⬇️
.../algorithms/time_evolution/bondenv/optimize_fet.jl	0.00% <0.00%> (ø)
src/states/infinitepeps.jl	58.97% <42.85%> (-11.03%)	⬇️
src/states/infiniteweightpeps.jl	0.00% <0.00%> (-93.34%)	⬇️
src/algorithms/time_evolution/bondenv/env_ctm.jl	0.00% <0.00%> (ø)
... and 5 more

... and 14 files with indirect coverage changes