Add (fast) full update

[Yue-Zhengyuan]

This PR tries again to add the fast full update algorithm (arXiv 1503.05345) (see also discussion in the old PR #106). It uses the unified interface for time evolution algorithms introduced in #280.

The performance of FU is benchmarked with the real-time evolution of the transverse field Ising model (TFIM) (see test/timeevol/tf_ising_realtime.jl), which calculates the magnetization in the x-direction after the infinite transverse field is reduced to a finite value.

In addition, I added the option to use pseudo-inverse to solve linear equations in ALSTruncation. Otherwise the test on TFIM will fail (but FullEnvTruncation is still fine with KrylovKit.linsolve).

Limitations:

• Current implementation does not support bipartite unit cell structure. We can try it later after proposals in [ENH] CTMRG arbitrary unit cell #207 are implemented. But it won't work for finite-T calculations anyway (?), so maybe it's not quite worth it...
• Only nearest neighbor Hamiltonians are supported (in principle support for next-nearest neighbor terms can be added; see arXiv 1711.07584).

To do later:

• Add support for PEPO evolution (the purification approach only).

[Yue-Zhengyuan]

@ogauthe You can now try the full update on models you are interested in. You can know the basic usage of the related functions from the test file test/timeevol/tf_ising_fu.jl.

[codecov]

Codecov Report

❌ Patch coverage is 18.21862% with 202 lines in your changes missing coverage. Please review.

Files with missing lines	Patch %	Lines
src/algorithms/time_evolution/fullupdate.jl	0.00%	178 Missing ⚠️
src/algorithms/ctmrg/sequential.jl	0.00%	15 Missing ⚠️
src/algorithms/contractions/bondenv/gaugefix.jl	0.00%	4 Missing ⚠️
src/algorithms/truncation/bond_truncation.jl	88.88%	3 Missing ⚠️
src/environments/ctmrg_environments.jl	0.00%	2 Missing ⚠️

Files with missing lines	Coverage Δ
src/PEPSKit.jl	100.00% <ø> (ø)
src/algorithms/contractions/bondenv/als_solve.jl	100.00% <100.00%> (ø)
src/algorithms/contractions/bondenv/benv_ctm.jl	100.00% <100.00%> (ø)
src/algorithms/truncation/fullenv_truncation.jl	97.01% <100.00%> (+0.04%)	⬆️
src/utility/svd.jl	87.69% <100.00%> (+0.19%)	⬆️
src/environments/ctmrg_environments.jl	71.89% <0.00%> (-0.79%)	⬇️
src/algorithms/truncation/bond_truncation.jl	95.18% <88.88%> (-1.84%)	⬇️
src/algorithms/contractions/bondenv/gaugefix.jl	87.50% <0.00%> (-12.50%)	⬇️
src/algorithms/ctmrg/sequential.jl	79.48% <0.00%> (-18.93%)	⬇️
src/algorithms/time_evolution/fullupdate.jl	0.00% <0.00%> (ø)

... and 7 files with indirect coverage changes

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[ogauthe]

Thank you! I will have a look.

[lkdvos]

@Yue-Zhengyuan , can you let me know what the status is on this (or other) PRs, and which ones should be reviewed/merged? I would like to consider releasing a new version of PEPSKit somewhere in the week of July 7th.

[Yue-Zhengyuan]

@lkdvos Right now we only have Sander's #184 and this one. #184 has been stagnated for quite a while, and maybe needs to be addressed first.

Fast full update is also ready for review actually. I'm just waiting for @ogauthe's feedback on whether it can provide enough improvement over SU for finite-T calculations.

[ogauthe]

I checked the finite temperature results obtained with full update as compared to simple update. See https://github.com/ogauthe/BenchmarkPEPS/blob/main/run/run_heisenberg_fullupdate.jl for the script.

I confirm I get the correct results with the full update. I find a slightly lower energy with the full update as compared to the simple update. Assuming energy(FU) = energy(SU) for beta < beta1 then energy(FU) < energy(SU) for beta > beta1 corresponds to a lower free energy, therefore a better approximation of the exact thermal density matrix. Congrat @Yue-Zhengyuan !

In terms of interface, I think ψ, env, = fu_iter2(fu_hamilt, ψ, env, fu_alg) can be improved. The function name could be more explicit and the interface (argument order) closer to simpleupdate. What about

simpleupdate(wpeps, hamilt, su_alg)
fullupdate(ψ, env, hamilt, fu_alg)

or

evolve_simpleupdate(wpeps, hamilt, su_alg)
evolve_fullupdate(ψ, env, hamilt, fu_alg)

or maybe

time_evolve(wpeps, hamilt, su_alg)
time_evolve(ψ, env, hamilt, fu_alg)

using dispatch on algorithm?

[Yue-Zhengyuan]

TL;DR: the name fu_iter2 can be improved, but I don't have the energy to unify the interface of FU, SU right now. SU can be completely revamped after belief propagation is implemented.

---

time_evolve(wpeps, hamilt, su_alg)
time_evolve(ψ, env, hamilt, fu_alg)

This can be a good improvement for future work. YASTN started on time evolution earlier than us and they have a unified interface for different algorithms. I didn't use it mainly because I'm more familiar with how TensorKit handles fermions. But currently I really don't have the energy for interface revamps to catch up with them...

In particular, fu_iter2 does not have an SU counterpart: it packs several FU steps together, because in fast FU we don't want to reconverge the CTMRG environment after every fu_iter.

Also, FU uses the usual InfinitePEPS, but SU uses InfiniteWeightPEPS. I actually regret writing SU in this way. Looking back on it, I only need to introduce SUWeight, which can later be generalized to BPEnv (#223). SU is actually FU with the bond environment given by the weights instead of the CTM tensors. After BPEnv is finished, we can unify SU, FU interface to

time_evolve(ψ::InfinitePEPS, env::BPEnv, H, alg::SimpleUpdate)
time_evolve(ψ::InfinitePEPS, env::CTMRGEnv, H, alg::FullUpdate)

[Yue-Zhengyuan]

Figured out what happened. Before adding the normalization, the fullinf env has a small norm. Since I use atol in truncerror, the resulting CTMRG bond dimension after truncation is smaller than it should be. This smaller bond dimension makes convergence of the environment easier and faster.

[Yue-Zhengyuan]

Commit history is becoming messy... Close this PR now and try again later.