ACE benchmarks on Paanini and figures - #20

Summary

Production ACE construction timings and figures from the Paanini workstation, plus two correctness fixes found while checking those runs against exact references.

Benchmarks

All new suites live under benchmark/ and share julia --project=benchmark. CSVs and figures are committed; C++ ACE is a separate clone and is not in the repo. Construction is single-threaded (julia -t 1, one OpenMP/BLAS thread). Methodology is in the folder READMEs.

Julia vs C++ (benchmark/JuliaVsC++/).

• Head-to-head build_process_tensor against Cygorek C++ ACE with dont_propagate.
• Central spin: $J=1$, $JT=20$, $J\Delta t=0.1$, $\varepsilon=10^{-10}$, $N_E\in{5,10,25,50,100}$, fully / partially / unpolarised baths, :zipup_cpp.
• Lorentzian spin-boson (Nat. Phys. 2022 SI grid, $C/\Omega^2=0.2$): $M=5$, $\Omega T=8$, $\varepsilon=10^{-8}$, $N_E\in{5,10,20,50,100}$, $k_BT/\Omega\in{0,0.5,1,3}$.
• Julia and C++ report the same $D_{\max}$ on every central-spin row (for example polarised $N=100$: both 13; unpolarised $N=10$: both 75).
• Julia build_s is lower throughout: polarised $N=5$ is 4.6 s vs 21 s, unpolarised $N=10$ is 117 s vs 1400 s. The same pattern holds for the spin-boson grid (vacuum $N_E=5$: 920 s vs 2300 s, both $D_{\max}=69$).
• Figure: benchmark/JuliaVsC++/results/julia_vs_cpp.pdf.
• Small sanity runs against joint ED give relative Frobenius errors $\sim 10^{-8}$ (central spin) and $\sim 10^{-5}$ (two-mode boson), with Julia–C++ disagreement another one to two orders smaller.

Compressor comparison (benchmark/ace_compressors/).
:zipup_cpp vs :canonzip at the same cutoff: unpolarised central-spin scaling in $N$, an eight-spin cutoff sweep (trajectory error vs a canonzip $\varepsilon=10^{-13}$ reference), and BLAS-thread scaling of one easy polarised central spin and one hard spin-boson PT. Figure: benchrk/ace_compressors/results/ace_compression.pdf.

SciPost Figure 1 (benchmark/scipost_fig1/). Four-mode $S_z\otimes S_z$ bath. Direct 32-dimensional ED is the $\Delta t$-free reference; Dense() is the exact PT; ACE uses :canonzip at $10^{-12}$. Panels compare timestep and propagation order. Figure: benchmark/scipost_fig1/results/fig1.pdf.

SciPost Figure 2 (benchmark/scipost_fig2/). Unpolarised central spin, $N=50$, one archived Xoshiro(20260905) bath for every $(\Delta t,\varepsilon)$. Panel (a) is the bond profile $D_k(t)$; panel (b) is $D_{\max}$ over $\Delta t\in{1.5,0.5,0.2,0.1,0.05}$ and $\varepsilon\in{10^{-6},\ldots,10^{-12}}$. Finer timesteps and tighter cutoffs raise $D_{\max}$ (for example $\Delta t=0.1$, $\varepsilon=10^{-6}$ gives $D_{\max}=4$; $\varepsilon=10^{-12}$ gives 42). Figure: benchmark/scipost_fig2/results/fig2.pdf.

Deprecation of :zipup

The previous default joined a mode ahead of truncation. That is not the C++ ACE schedule. The C++ forward pass truncates the current core before the next timestep is joined, then sweeps backward.
:zipup is removed. ACE(; compression) is now :zipup_cpp (default) or :canonzip. :zipup_cpp is that truncate-then-join order with the ITensors default SVD (gesdd). Passing :zipup throws and names :zipup_cpp. Compressor figures and examples were regenerated on this interface. This is a pre-1.0 keyword break; the package version stays 0.2.0.

Bug fixes

PT-vs-full-ED tests were loose enough that a reversed bath channel looked like Trotter error.

• Single-mode bath MPOs wired the Liouvillian input and output backwards relative to liouvillian_propagator_itensor, so the contracted channel was time-reversed. prime(env) is now the left (input) bond and env the right (output) bond.
• Multimode Dense cores had the fused bath input/output combiners swapped relative to the one-mode builder, so non-commuting baths were not trace-preserving. Those links follow the same chronological convention.
  Tests now compare $\rho_{\mathrm{PT}}$ to the same discrete split propagator at $\sim 10^{-11}$. Disagreement with $e^{-itH}$ is reported separately as Trotter error. Dense and ACE are also checked against that split schedule on random Hermitian baths.

Test plan

• CI

• bench: correctness of builders against discretisation methods

• bench: compression using cutoff and timestep

• chore: format README latex expressions correctly

• fix: restore chronological bath bonds in process-tensor cores

• test: silence package logs in the test suite

• feat: drop :zipup compressor and make :zipup_cpp the default ACE compression

• fix: restore chronological fused-bath links in Dense PTs

• bench: add Julia vs C++ ACE construction comparison

• bench: use a shared --project=benchmark environment

• chore: add links to files in benchmark READMEs

• chore: larger fonts in plots