Pith. Sign in

REVIEW

Performance Benchmarking: Software for the Density Matrix Renormalization Group

PaperPDF from arXiv

data files

ReviewThe objections and verdict, as JSON Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
X Bluesky LinkedIn Reddit Hacker News
Per Sehlstedt, Paolo Bientinesi, Lars Karlsson

Computational Physics · Submitted 30 Jul 2026 · 84 references

Pith's verdict: Solid multi-package DMRG cost-vs-quality benchmarks with real spreads and a usable framework; scope is deliberately narrow but the claims match the data.

T0 · AI review

How this review was made: An AI referee (grok-4.5) read the paper on July 31, 2026 and answered a fixed list of questions about it. T0 is the starting level every paper gets. The levels describe how deeply Pith has checked the paper, never the authors.

  1. T0 AI review An AI read the paper and answered a fixed list of questions.
  2. T1 Audit Automatic checks that the references and files the paper relies on exist and match.
  3. T2 Compute The paper's code or calculations re-run with the same results.
  4. T3 Formal statement The claims written out in a formal math language a computer can read.
  5. T4 Proof Those claims proved, and the proof checked by computer.

How Pith checks papers →

· 6 minor · Ask about this paper · Read the full review →
Challenge this review Comment (0) Read on arXiv ↗
Cite ▾
arXiv ID2607.28369 (version 1)
Pith IDJCZAGCPI, Pith's permanent record of this paper and its review
CitationLars Karlsson, Paolo Bientinesi, Per Sehlstedt. "Performance Benchmarking: Software for the Density Matrix Renormalization Group." arXiv:2607.28369 (2026). https://pith.science/paper/JCZAGCPI
Cite this reviewBibTeX for Pith's review of this paper
Claim paper

Why Pith says this

Highlight any text to comment on it.

Referee report

How Pith checks papers → · Full audit of this paper →

The paper

The paper claims

DMRG software packages differ by up to two orders of magnitude in time-to-accuracy, and so do different settings inside one package.

The reading

The density matrix renormalization group (DMRG) is a workhorse method for quantum many-body problems, yet more than fifty software packages implement it with almost no shared standard for comparing how fast they reach a given accuracy. This paper argues that meaningful comparison requires jointly tracking computational cost and solution quality, using the same models, controlled parameters, and controlled hardware, and measuring end-to-end behavior rather than isolated sweep times. Applying that framework to eight open-source packages on three standard one-dimensional lattice models, the authors find large gaps: packages can differ by factors of four to twenty (and in places nearly two orders of magnitude) in wall time to a target energy error even when settings are aligned, while changing Krylov dimension, floating-point precision schedule, 1-site versus 2-site updates, or subspace expansion inside a single package can produce comparable or larger swings. The practical message is that rigorous, cost-versus-quality benchmarking is itself a research tool: it exposes non-obvious trade-offs, shows that strategy often matters as much as package choice, and gives users and developers a shared baseline for deciding what to run and what to improve next.

What carries the argument

A performance-oriented benchmarking framework whose five requirements are joint cost–quality evaluation, end-to-end metrics, common model problems, controlled parameter configurations, and controlled hardware/software environments; operationalized here as wall time versus relative energy residual on L=100 open chains for three lattice models.

Extended reading notes

Core claim

When computational cost and solution quality are evaluated jointly under controlled models, parameters, and hardware, DMRG implementations differ by up to two orders of magnitude in time-to-accuracy—both across packages with aligned settings and within one package under different parameter configurations. Sweep time alone is an incomplete metric; end-to-end wall time versus relative energy error is required for meaningful ranking.

Load-bearing premise

That simple fixed, aligned baseline settings on single-core one-dimensional chains of length 100 are enough to support general comparative claims about package performance, even though specialized features and per-package optimal tuning are deliberately left unused.

Editorial extensions

If this is right

  • Users choosing a DMRG package should treat time-to-target-accuracy curves, not advertised sweep speed or feature lists alone, as the primary decision data.
  • Developers gain more by exposing tunable, switchable strategies (precision, update mode, expansion) than by micro-optimizing a single fixed path.
  • Future package papers can adopt the five-requirement checklist so new claims become cross-comparable instead of isolated scaling plots.
  • Parameter-tuning effort can rival or exceed package choice in impact, so automated or default-adaptive schedules become high-value targets.
  • The same cost–quality framing can be reused for other tensor-network families beyond MPS-DMRG.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If strategy flexibility dominates package identity, community effort on interoperable schedule languages or shared backends may pay off more than proliferating new full stacks.
  • The large within-package swings suggest that published ‘default’ timings systematically understate what experienced users can achieve and overstate differences between codes.
  • Extending the suite to two-dimensional lattices, quantum-chemistry Hamiltonians, or multi-node/GPU runs would test whether the same ranking and sensitivity patterns survive outside the 1D condensed-matter regime used here.
Original abstract

The performance of scientific software often determines the scale of problems that can be solved in practice. As multiple implementations of the same algorithm emerge, systematic evaluation is needed to compare their strengths and limitations. The density matrix renormalization group (DMRG) algorithm, widely used to study quantum systems, has over 50 software implementations. These implementations vary in multiple aspects that can strongly affect performance. However, despite the need, performance evaluations of these implementations are scarce and lack a consistent standard; many existing evaluations are either too incomplete to enable meaningful comparisons or focus on objectives other than direct performance comparisons, thereby limiting understanding of how the implementations compare. Here, we present a performance-oriented benchmarking framework to facilitate meaningful comparisons of DMRG implementations, and we apply it to quantify the performance of eight implementations, highlighting similarities and differences among them. Furthermore, we examine multiple parameter settings, optimization strategies, and implementation-specific features to demonstrate how parameter configuration can affect performance and how systematic evaluation can reveal non-obvious trade-offs. The results show significant performance differences, up to two orders of magnitude in some cases, not only between different implementations when aligning parameters, but also within the same implementation when comparing different parameter configurations. Hence, our results demonstrate the significant value and insight that can be gained from conducting rigorous performance evaluations. Using our results and framework as a starting point, more rigorous benchmarking will ultimately help users and developers make informed decisions and support future development efforts to build better, more efficient software.

Figures
Figure 1. Performance of DMRG implementations on the transverse-field Ising
Figure 2. Performance of DMRG implementations on the isotropic spin-1
Figure 3. Performance of DMRG implementations on the Fermi–Hubbard model
Figure 4. Performance of MPSKit on the transverse-field Ising model using different Krylov subspace dimensions. 5.2.2 Mixed-precision In
Figure 5. Performance of ITensorMPS on the Fermi–Hubbard model using three different floating-point precision strategies: single-precision only, double￾precision only, and starting with single- and switching to double-precision after four sweeps. Because the single-precision Hamiltonian yields lower energy due to numerical imprecision, the single-precision result error is calculated as an absolute difference in eq. (11) rather than a linear one. becomes necessary, we retain the fast initial convergence while still reaching the same final accuracy as the full double-precision run. In this way,…
Figure 6. Performance of YASTN on the Fermi-Hubbard model using three update mode strategies: 1-site only, 2-site only, and alternating 1-site and 2- site. dimension because it is more computationally cost-effective than the 2-site method. Still, it becomes stuck in a suboptimal configuration, as it tends to do when symmetries are enforced, and it reaches only an accuracy of 10−5 . More￾over, since the traditional 1-site method cannot dynamically increase the bond dimension, it requires starting with the target bond dimension, which can be inefficient during the early stages of the…
Figure 7. Performance of TeNPy on the Fermi-Hubbard model using 2-site DMRG and 1-site DMRG with and without subspace expansion. To start, we again observe the typical drawbacks of the traditional 1-site method, i.e., the need to start at the target bond dimension and the tendency to get stuck in local minima when enforcing symmetries, in this case, resulting in only 10−2 accuracy after approximately 200 s. In contrast, the SSE approach largely avoids both issues, achieving an accuracy of nearly 10−10 in just under 140 s. Moreover, we observe that the SSE approach offers a competitive…

Figures reproduced from arXiv:2607.28369 by the authors.

References

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.