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PEPSKit.jl: A Julia package for projected entangled-pair state simulations

T0 review · 0 major / 1 minor · reviewed 2026-06-30 · grok-4.3

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Pith's one-line read PEPSKit.jl supplies high-level algorithms for infinite projected entangled-pair state simulations of two-dimensional quantum systems with symmetry support.

desk verdict PEPSKit.jl is a straightforward Julia port of iPEPS with added non-Abelian and fermionic symmetry support that fills a niche for users already in that ecosystem. read the letter →

arxiv 2605.19960 v2 pith:6RUOETN7 submitted 2026-05-19 cond-mat.str-el physics.comp-phquant-ph

Paul Brehmer , Lander Burgelman , Zheng-Yuan Yue , Gleb Fedorovich , Jutho Haegeman , Lukas Devos This is my paper · ORCID
classification cond-mat.str-elphysics.comp-phquant-ph
keywords projectedentangled-pairstatesiPEPSJuliapackagequantummany-bodysystemstensornetworkssymmetriesfermionicground-statesimulations
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper presents a Julia package for simulating two-dimensional quantum many-body systems using infinite projected entangled-pair states. It supplies algorithms that handle Abelian and non-Abelian symmetries as well as fermionic systems. The package includes tools for ground-state searches, real-time evolution, and finite-temperature calculations on multiple lattice geometries. A reader would care because these methods let researchers model strongly correlated materials in two dimensions where exact solutions are rare.

What carries the argument

The PEPSKit.jl package, which implements the high-level iPEPS algorithms that incorporate support for Abelian, non-Abelian, and fermionic symmetries.

What would settle it

Running a benchmark on a standard two-dimensional model such as the Heisenberg antiferromagnet, then comparing the package output to results from an independent established method, would test whether the implementations match known values.

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Extended reading notes

Core claim

The authors state that PEPSKit.jl builds on tensor computations to deliver high-level algorithms for iPEPS simulations. These algorithms support both Abelian and non-Abelian symmetries together with fermionic systems and enable ground-state, time-evolution, and finite-temperature simulations in systems with different physical symmetries and lattice geometries. The features are shown through examples and technical benchmarks.

Load-bearing premise

The high-level algorithms are implemented correctly and produce accurate results for the claimed symmetries and system types.

Editorial extensions

If this is right

  • Ground-state properties of two-dimensional models with symmetries become computable at scale.
  • Time evolution of fermionic systems on lattices can be followed without manual symmetry handling.
  • Finite-temperature observables are accessible for a range of lattice geometries.
  • Users gain the ability to switch between different symmetry sectors within the same simulation framework.

Reading between the lines

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

  • The package structure may allow straightforward addition of new lattice types or interaction terms by other developers.
  • Researchers could use it to scan phase diagrams across symmetry classes that were previously hard to access uniformly.
  • Integration with existing Julia tensor libraries could reduce setup time for hybrid classical-quantum studies.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

0 major / 1 minor

Summary. The manuscript presents PEPSKit.jl, a Julia package for simulating two-dimensional quantum many-body systems with infinite projected entangled-pair states (iPEPS). It builds on TensorKit.jl to provide high-level algorithms supporting Abelian and non-Abelian symmetries as well as fermionic systems, covering ground-state, time-evolution, and finite-temperature simulations on various lattice geometries, with these capabilities illustrated through examples and technical benchmarks.

Significance. If the package implements the described features correctly and remains publicly available with reproducible examples, the work supplies a useful open-source tool in the Julia ecosystem for tensor-network studies of strongly correlated systems. The emphasis on symmetry support and the provision of reproducible code and benchmarks constitute a clear strength for the condensed-matter simulation community.

minor comments (1)
  1. The abstract contains the string "PEPSKit$.$jl"; this appears to be a LaTeX formatting artifact and should be rendered consistently as PEPSKit.jl throughout the manuscript.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive review of the manuscript, their recognition of the package features (including symmetry support for Abelian/non-Abelian and fermionic systems, as well as ground-state, time-evolution, and finite-temperature algorithms), and for recommending acceptance. No major comments were raised that require addressing.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity

full rationale

The manuscript is a software package announcement describing PEPSKit.jl for iPEPS simulations. It contains no derivations, equations, predictions, fitted parameters, or load-bearing self-citations that reduce to inputs by construction. Claims rest on the public availability of the package and reproducibility of provided examples/benchmarks, which are externally verifiable without circular logic. This is a standard, non-circular software description.

Assumptions & free parameters 0 free parameters · 0 assumptions · 0 invented entities

No scientific derivation or physical model is advanced; the document is a software-package description. Consequently the ledger contains no free parameters, axioms, or invented entities.

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Cite this review

Pith. "Pith review of PEPSKit.jl: A Julia package for projected entangled-pair state simulations." pith.science (2026). https://pith.science/paper/6RUOETN7

@misc{pith2026260519960,
  author       = {Pith},
  title        = {Pith review of: PEPSKit.jl: A Julia package for projected entangled-pair state simulations},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6RUOETN7}},
  note         = {Machine review of arXiv:2605.19960}
}
abstract

We present PEPSKit$.$jl, a Julia package for simulating two-dimensional quantum many-body systems with infinite projected entangled-pair states (iPEPS). PEPSKit$.$jl builds on the TensorKit$.$jl package for tensor computations and provides high-level algorithms for iPEPS simulations that support both Abelian and non-Abelian symmetries, as well as fermionic systems. This work gives an overview of the main package features, which include support for ground-state, time-evolution, and finite-temperature simulations in systems with different physical symmetries and lattice geometries. These capabilities are illustrated through various examples and technical benchmarks.

Figures

Figures reproduced from arXiv: 2605.19960 by the authors.

Figure 1
Figure 1. Bond environment tensor for (a) the simple update scheme (which can be [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
Figure 2
Figure 2. Truncation of internal virtual bonds (red) in the 3-site cluster regarded as [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Finite temperature x-magnetization 〈Sx 〉 and energy per site E of the trans￾verse field Ising model from Eq. (27) with J = 1/4 obtained using simple update with the same settings as the TeNeS simulations of Ref. 34. The Trotter evolution step is ∆β = 0.02 for the first 50 steps, 0.01 for the following 200 steps, and 0.1 for the final 10 steps. The bond dimensions are chosen in accordance with [34] at D = 10 for the … view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: Energy of the J1 -J2 model at finite temperature for (a) J2/J1 = 0 and (b) J2/J1 = 0.5, obtained from simple update with SU(2) symmetry. The Trotter evolution step size is chosen at ∆β = 0.001. The bond dimensions are D ≈ 7 for the iPEPO, and χ = 21 for the CTMRG envir…
Figure 5
Figure 5. Figure 5: Energies (a) and magnetizations (b) of the square lattice [PITH_FULL_IMAGE:figures/full_fig_p013_5.png]
Figure 6
Figure 6. Figure 6: Optimized energies as a function of inverse iPEPS bond dimension (cor [PITH_FULL_IMAGE:figures/full_fig_p016_6.png]
Figure 7
Figure 7. Figure 7: Planar projection of the magnetization in the Fermi-Hubbard model on the [PITH_FULL_IMAGE:figures/full_fig_p016_7.png]
Figure 8
Figure 8. Figure 8: Time (in seconds) per CTMRG iteration for contracting the ground state of [PITH_FULL_IMAGE:figures/full_fig_p017_8.png]

Review history (2 revisions) →

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Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Robust spin pseudogap and spin-charge separation in the $\sigma t$-$J$ model

    cond-mat.str-el 2026-08 conditional novelty 6.0 of 10

    The σt-J model is found to keep its spin pseudogap and spin-sector BKT transition almost doping-independent, which a slave-fermion mean-field theory with a PSG-selected ansatz explains as spin-charge separation.

  2. Implicit differentiation of tensor network algorithms

    quant-ph 2026-07 conditional novelty 6.0 of 10

    PEPS energy gradients can be computed by implicit differentiation of characteristic equations for the contraction environment, avoiding unstable subroutine backpropagation and reducing asymptotic cost.

Reference graph

Works this paper leans on

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    " write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 gl...

Pith tools

Reviewed June 30, 2026 · model on record in the stance chip above.