Add 3-site simple update (aka 3-site cluster update) by Yue-Zhengyuan · Pull Request #171 · QuantumKitHub/PEPSKit.jl

Yue-Zhengyuan · 2025-04-09T03:39:35Z

This PR adds the 3-site simple update (aka 3-site cluster update; see discussion in Issue #164), which can handle Hamiltonians containing up to next nearest neighbor terms (e.g. the J1-J2 model).

It convert the Hamiltonian from LocalOperator format to a bunch of 3-site MPOs acting on the clusters. Relevant functions are added in src/algorithms/time_evolution/evoltools.jl.
Truncation of bonds in the 3-site cluster after applying the time evolution gate is done using some "projectors" (I didn't bother to customize OBC MPS algorithms from MPSKit to suit my needs). Their construction is explained in detail in the beginning of the file src/algorithms/time_evolution/simpleupdate3site.jl. It is tested in the new test file test/timeevol/cluster_projectors.jl.
Added an J1-J2 model SU example at examples/heisenberg_evol/j1j2.jl. We may also consider using the 3-site SU to provide initialization in the J1-J2 AD test. But note that the 3-site SU also requires a minimal unit cell size (2, 2) (in addition, bipartite structure is now not allowed), while the AD test currently uses 1-site unit cell with C4v symmetry.

This is kind of a large unseparated PR. Suggestions are welcome. I'm still testing fermion models, so the code is not finalized yet.

codecov · 2025-04-09T03:43:48Z

Codecov Report

Attention: Patch coverage is 96.74419% with 7 lines in your changes missing coverage. Please review.

Files with missing lines	Patch %	Lines
src/operators/localoperator.jl	53.84%	6 Missing ⚠️
src/algorithms/time_evolution/evoltools.jl	97.29%	1 Missing ⚠️

Files with missing lines	Coverage Δ
src/PEPSKit.jl	`100.00% <ø> (ø)`
src/algorithms/time_evolution/simpleupdate.jl	`100.00% <100.00%> (+13.04%)`	⬆️
src/algorithms/time_evolution/simpleupdate3site.jl	`100.00% <100.00%> (ø)`
src/algorithms/time_evolution/evoltools.jl	`98.36% <97.29%> (-1.64%)`	⬇️
src/operators/localoperator.jl	`69.09% <53.84%> (+7.88%)`	⬆️

... 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 · 2025-04-13T11:25:11Z

I further added a test to compare the SU and 3-site SU energy for the Hubbard model without next-nearest neighbor terms (they should be close). I think the code is now ready for fermions.

lkdvos

I left some general comments throughout, keep in mind that I do not have much experience with the algorithm itself so I definitely might be missing some things or getting things wrong.
As always though, this is an impressive amount of work, and a great addition.

Co-authored-by: Lukas Devos <ldevos98@gmail.com>

pbrehmer · 2025-05-14T17:48:53Z

AD optimization seems to work but it has some hickups at some point due to linesearching. I will try to improve that tomorrow. I also extended the commentary in the J1-J2 example a bit to make it similar style-wise to other examples.

pbrehmer · 2025-05-15T13:08:07Z

I decided to just restrict the maxiter of the optimization since the AD-optimized estimate already improves the SU estimate quite a bit and a proper full optimization would probably take long and be more complicated. I added the rendered example as well, so it should show up in the docs now. Ready to merge for me!

Yue-Zhengyuan · 2025-05-15T14:33:43Z

@pbrehmer I'm glad to see that with SU initialization the AD energy is lower than YASTN result, so maybe a good initialization does help. How does the energy compare with the AD optimization with just 1x1 unit cell starting from random initialization?

pbrehmer · 2025-05-16T15:26:27Z

I was also happy to see that! Actually, on a 1x1 unit cell from random initialization, I'm having a lot of trouble to optimize the PEPS. There, I'm encountering degenerate singular values sometimes and CTMRG sometimes struggles to converge during optimization such that the linesearch fails. I also tried Lander's backtracking linesearch algorithm and also there I'm having problems.

So my feeling is that the SU-evolved PEPS is actually quite a nice starting point for the AD optimization. I'll try to optimize that fully (up to higher accuracy) but I suspect that the environment dimension might be a little low for that - for small chi, PEPS optimization runs tend to get stuck at some point.

Yue-Zhengyuan · 2025-05-16T15:44:15Z

Looking at YASTN data, the first line is

# uuid CTM_BFGS100LS_U1B_D4-chi96-j20.5-run0-c2U1BD4j2045chi96n0

So he is already using $\chi = 96$. Then he measure the optmized state with various $\chi$'s, and the energy converges to 1e-6 precision for $\chi \gtrsim 128$. Indeed a large $\chi$ is necessary. Maybe now IterSVD can be used to speed up the optimization?

In the calculation he also imposes the geometric $C_{4v}$ symmetry to the 1x1 unit cell in addition to a sub-lattice spin rotation, which further reduces the number of parameters. Did you do this for the 1x1 optimization before?

pbrehmer · 2025-05-16T15:57:32Z

Indeed! I'm not yet sure if IterSVD already pays off here with D=4 but in any case we can push the environment dimension quite a bit. I didn't impose $C_{4v}$ symmetry but I'll try that next. Of course we don't have proper $C_{4v}$ CTMRG yet because the environment should consist only of one corner and edge tensor (per unit cell entry). But I'm thinking that we should implement that anyway at some point (also if we want to run proper benchmarks).

lkdvos

Left some small comments, but in general this looks almost good to go for me!

lkdvos · 2025-05-21T14:11:04Z

+
+Let's start by initializing an `InfiniteWeightPEPS` for which we set the required
+parameters as well as physical and virtual vector spaces. Since the $J_1$-$J_2$ model has
+*next*-neighbor interactions, the simple update algorithm requires a $2 \times 2$ unit cell:


Suggested change

*next*-neighbor interactions, the simple update algorithm requires a $2 \times 2$ unit cell:

*next*-nearest-neighbor interactions, the simple update algorithm requires a $2 \times 2$ unit cell:

Also, I'm slightly confused by this explanation: for me this sounds like next-nearest neighbor hamiltonians have a 2x2 unitcell ground state.
In principle the Hamiltonian still has a translation symmetry for a single site, so I don't think it follows automatically that you would need a $2x2$ unit cell for a next-nearest-neighbour hamiltonian.
From what I understand, this is mostly an algorithmic restriction, and is a result of using simple update, so maybe we can slightly reword this to make that more obvious?

Indeed it's an algorithm limitation. I'll make this point more clear.

lkdvos · 2025-05-21T14:16:09Z

+    H = real( ## convert Hamiltonian `LocalOperator` to real floats
+        j1_j2_model(ComplexF64, symm, InfiniteSquare(Nr, Nc); J1, J2, sublattice=false),
+    )


Suggested change

H = real( ## convert Hamiltonian `LocalOperator` to real floats

j1_j2_model(ComplexF64, symm, InfiniteSquare(Nr, Nc); J1, J2, sublattice=false),

)

H = j1_j2_model(Float64, symm, InfiniteSquare(Nr, Nc); J1, J2, sublattice=false)

I know this used to fail since we tried to construct Sy, was this not fixed in the meantime?

No, I still cannot directly set T = Float64 because of S_y in MPSKitModels v0.4.2.

lkdvos · 2025-05-21T14:20:28Z

+Compute `exp(-dt * H)` from Hamiltonian `H`.
+Each term in `H` must be a single `TensorMap`.


This is a bit misleading, given that this is not actually the full exponential of the hamiltonian, but rather a weird intermediate struct we use that represents sum(exp(-h * dt) for h in H) but is not used that way. (in particular, exp(sum) would be prod(exp), not sum(exp)). I don't have any issues with reusing LocalOperator that way, I would just reword the docstring.

lkdvos · 2025-05-21T14:22:15Z

+Check if a Hamiltonian contains only nearest neighbor terms
+"""
+function is_nnham(H::LocalOperator)


Suggested change

Check if a Hamiltonian contains only nearest neighbor terms

"""

function is_nnham(H::LocalOperator)

is_nearest_neighbour(H)

Check if an operator contains only nearest neighbor terms

"""

function is_nearest_neighbour(H::LocalOperator)

In general I think using longer names might be easier to read here, but I don't feel that strongly about it.
Adding the signature in the docstring is a good idea though

Are we following the British spelling in the repo? (neighbour instead of neighbor) But I also see that center instead of centre is used...

I think British and American spelling are mixed throughout the repo, so at this point you can use what you prefer. (Perhaps we can unify at some point but I dont think that's a super high-priority issue right now.)

Then I just follow whatever is already in the repo.

Yue-Zhengyuan · 2025-05-22T04:37:40Z

@pbrehmer I tried to regenerate the J1-J2 SU example by deleting the entry in examples/Cache.toml and run julia examples/make.jl, but it still tries to generate all examples. Can you help look at this?

pbrehmer · 2025-05-22T09:44:34Z

Alright this seems to be good to go now!

Regarding the example cache: I think that the caching is somehow broken when running the examples from a forked repository. This might be because @__DIR__ returns an absolute path which is then used in the checksum. (The absolute paths are of course different for different users.) I need to clean up this caching mechanism at some point and then I'll take care of that. I'll do that in a separate PR once I find the time/need!

Add 3-site simple update

6f385f3

Yue-Zhengyuan added 6 commits April 10, 2025 09:03

Merge remote-tracking branch 'upstream/master' into su-nnn

a539e18

Update SU examples

d684e8d

Add test to check consistency of SU and 3-site SU on Heisenberg model

f4e671a

Merge remote-tracking branch 'upstream/master' into su-nnn

8ee4612

Fix formatting

8a6551d

Merge remote-tracking branch 'upstream/master' into su-nnn

a202b47

Yue-Zhengyuan mentioned this pull request Apr 13, 2025

Wrap SU intermediate steps into functions #143

Merged

Yue-Zhengyuan added 2 commits April 13, 2025 13:43

Define normalize! for InfinitePEPS

1683d12

Update test and docstring on cluster canonical form

942d944

lkdvos reviewed Apr 13, 2025

View reviewed changes

Yue-Zhengyuan and others added 13 commits April 14, 2025 00:15

Define real, imag for LocalOperator

6aa5b81

Gate MPO now acts on cluster from below

e8ab176

Fix formatting

84c9541

Improve type stability of cluster, projector list

6e0eb4e

Improve normalize for InfinitePEPS

87d49a1

Co-authored-by: Lukas Devos <ldevos98@gmail.com>

Add test on imag for LocalOperator

87b4606

Merge remote-tracking branch 'origin/real-imag-localop' into su-nnn

b2978ba

Simplify conversion to real Hamiltonian

d41ea96

Fix formatting

0825212

Use flip to reverse arrows for SVD result

cd8ad25

Make type annotation more precise

0281c91

Use NamedTuple to store gatempo

dcb20bf

Remove definition of normalize! for InfinitePEPS

56059f3

Yue-Zhengyuan commented Apr 14, 2025

View reviewed changes

Comment thread src/algorithms/time_evolution/simpleupdate3site.jl Outdated

Yue-Zhengyuan added 3 commits April 14, 2025 16:30

Remove unused variable

0991196

Improve type stability

d32ed5c

Merge upstream/master

52458e9

Merge branch 'master' into su-nnn

493f8cd

pbrehmer added 2 commits May 15, 2025 14:55

Add rendered J1-J2 example

d614c8b

Fix docs issues

da04a1d

Fix formatting

f342458

Merge branch 'master' into su-nnn

69c8a67

lkdvos reviewed May 21, 2025

View reviewed changes

Yue-Zhengyuan added 6 commits May 22, 2025 11:52

Replace /= norm with normalize!

9e35dcf

Update example and add reference

8d82c73

Improve get_expham and is_nearest_neighbour

5b95378

Apply suggestion

d867cc5

Merge remote-tracking branch 'upstream/master' into su-nnn

910e44c

Fix British spelling

a3c0acf

Yue-Zhengyuan and others added 3 commits May 22, 2025 15:08

Fix test

91c7a05

Update J1-J2 example and rendered files

20cfe4a

Fix bib DOI entry

0bc9a24

pbrehmer requested a review from lkdvos May 22, 2025 09:45

lkdvos approved these changes May 22, 2025

View reviewed changes

pbrehmer merged commit 1c1d1f7 into QuantumKitHub:master May 22, 2025
45 checks passed

Yue-Zhengyuan deleted the su-nnn branch May 23, 2025 01:21

ogauthe mentioned this pull request May 28, 2025

[discussion] CTMRG performances #205

Open

ogauthe mentioned this pull request Jun 9, 2025

2nd neighbor simple update results #215

Closed

Yue-Zhengyuan mentioned this pull request Jun 14, 2025

Fix 3-site SU dt and reduce artificial C4v breaking #219

Merged

	next-neighbor interactions, the simple update algorithm requires a $2 \times 2$ unit cell:
	next-nearest-neighbor interactions, the simple update algorithm requires a $2 \times 2$ unit cell:

		Compute `exp(-dt * H)` from Hamiltonian `H`.
		Each term in `H` must be a single `TensorMap`.

-Check if a Hamiltonian contains only nearest neighbor terms
-"""
-function is_nnham(H::LocalOperator)
+    is_nearest_neighbour(H)
+Check if an operator contains only nearest neighbor terms
+"""
+function is_nearest_neighbour(H::LocalOperator)

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