pith. sign in

arxiv: 2606.23657 · v1 · pith:TOS45WPOnew · submitted 2026-06-22 · ❄️ cond-mat.str-el

Resolving support-mismatch by local basis rotation in variational Monte Carlo

Jia-Lin Chen , Zhen Fan , Canhui Yan , Yantao Wu , Tao Xiang This is my paper

Pith reviewed 2026-06-26 06:24 UTC · model grok-4.3

classification ❄️ cond-mat.str-el
keywords variational Monte Carlosupport mismatchlocal basis rotationquantum quench dynamicsreal-time evolutiondynamical structure factorcondensed matter simulation
0
0 comments X

The pith

A local rotation of the sampling basis restores full support after a charged local operator in variational Monte Carlo.

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

Variational Monte Carlo calculations of real-time dynamics after a local quench are blocked by support mismatch: the charged operator forces an exponentially large fraction of sampled configurations to zero weight, freezing the evolution at the first step. The paper argues that this mismatch is itself a local effect generated by the operator. A local rotation of the sampling basis restores the missing configurations without changing the variational dynamics or introducing new biases. The resulting scheme integrates into existing algorithms and yields accurate long-time dynamics for dynamical structure factors in one dimension and local quenches in two dimensions. The same rotation approach is claimed to extend to ground-state variational Monte Carlo.

Core claim

The support mismatch generated by a charged local operator is itself local. Rotating the sampling basis locally restores the missing support, allowing unbiased real-time evolution after the quench while leaving the underlying variational dynamics unchanged.

What carries the argument

Local basis-rotation sampling scheme that applies a local unitary rotation to the chosen sampling basis to recover configurations eliminated by the quench operator.

If this is right

  • VMC can now compute dynamical structure factors in one dimension.
  • Unbiased local-operator quench dynamics become accessible in two dimensions.
  • The rotation scheme integrates directly into existing variational Monte Carlo codes.
  • The same local-rotation idea may improve ground-state variational Monte Carlo sampling.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If locality of the mismatch holds for other operators, the method could apply to a wider class of time-dependent problems.
  • The approach highlights that sampling-basis choice can be adjusted locally without global changes to the wave-function ansatz.
  • In higher dimensions the cost of identifying the local rotation may grow, suggesting a possible trade-off between locality and computational overhead.

Load-bearing premise

The support mismatch created by the charged local operator remains sufficiently local that a local basis rotation can restore it without new sampling biases.

What would settle it

Run the rotated-basis scheme on a small exactly solvable 1D chain after a local quench and check whether the computed real-time correlators match the exact diagonalization result at long times.

Figures

Figures reproduced from arXiv: 2606.23657 by Canhui Yan, Jia-lin Chen, Tao Xiang, Yantao Wu, Zhen Fan.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematic illustration of dynamical freezing and its [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Time evolution of the quench-site magnetization [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Dynamical structure factor [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Time evolution of the quench-site magnetization [PITH_FULL_IMAGE:figures/full_fig_p005_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Local-operator-quench dynamics of the 8 [PITH_FULL_IMAGE:figures/full_fig_p006_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: compares the two optimization methods for the ground-state energy optimization of the 4 × 4 peri￾odic square-lattice J1–J2 model at the frustrated point J2/J1 = 0.5, with the sign match during optimization shown in the inset. To isolate sampling effects from the expressivity limitations of the ansatz and optimiza￾tion difficulties associated with a complex energy land￾scape, we use a full lookup-table wave… view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Full-summation diagnostics of estimator bias. Di [PITH_FULL_IMAGE:figures/full_fig_p009_9.png] view at source ↗
read the original abstract

Real-time dynamics after a local quench by a charged operator encodes the response functions measured in spectroscopic experiments, yet they have long posed a challenge for variational Monte Carlo calculations. The obstacle is a support mismatch: the projective action by a charged local operator forces an exponentially large number of configurations to vanish, but these configurations may still contribute to the dynamics, biasing the estimators and freezing the evolution at the very first step. This difficulty is an artifact of the chosen sampling basis, and the support mismatch generated by a charged local operator is itself local. We demonstrate that the missing support can be restored by a local rotation of the sampling basis, without changing the underlying variational dynamics. We propose a local basis-rotation sampling scheme that resolves the support-mismatch problem and can be readily incorporated into existing variational Monte Carlo algorithms. Benchmarks show that rotation sampling accurately captures long-time quantum dynamics, enabling variational Monte Carlo calculations of dynamical structure factors in one dimension and unbiased local-operator quench dynamics in two dimensions. We also show that this resolution of the support-mismatch problem extends beyond real-time dynamics, and may also be helpful for ground state variational Monte Carlo calculations.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 0 minor

Summary. The paper claims that support mismatch in variational Monte Carlo for real-time dynamics after local quenches by charged operators arises as an artifact of the sampling basis; because the mismatch generated by a charged local operator is itself local, a local rotation of the sampling basis restores full support without changing the underlying variational wavefunction or dynamics. The method is implemented as a local basis-rotation sampling scheme integrable into existing VMC algorithms and is benchmarked on dynamical structure factors in one dimension and local-operator quench dynamics in two dimensions, with an additional claim of utility for ground-state calculations.

Significance. If the numerical evidence holds, the technique removes a long-standing bias in VMC estimators for post-quench dynamics and response functions, enabling previously inaccessible calculations in strongly correlated systems while preserving unbiased sampling with respect to the original variational projector. The explicit construction, locality argument, and compatibility with existing codes constitute practical strengths.

major comments (1)
  1. [Benchmarks] Benchmarks section: the assertion that rotation sampling 'accurately captures long-time quantum dynamics' is not accompanied by error bars on the reported quantities, direct baseline comparisons against exact or known results, or an explicit description of how post-quench estimators are constructed; these omissions make it impossible to verify that the central claim of unbiased long-time evolution has been demonstrated.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading, positive assessment of the work, and recommendation for minor revision. We address the major comment below.

read point-by-point responses

  1. Referee: Benchmarks section: the assertion that rotation sampling 'accurately captures long-time quantum dynamics' is not accompanied by error bars on the reported quantities, direct baseline comparisons against exact or known results, or an explicit description of how post-quench estimators are constructed; these omissions make it impossible to verify that the central claim of unbiased long-time evolution has been demonstrated.

    Authors: We agree that the benchmarks section would be strengthened by the inclusion of statistical error bars, direct comparisons to exact or known results (such as ED or DMRG for the 1D cases), and an explicit description of the post-quench estimator construction. In the revised manuscript we will add error bars to all reported dynamical quantities, include baseline comparisons where feasible, and expand the methods section with a detailed account of how the estimators are formed after the local quench. These changes will make the verification of unbiased long-time evolution explicit. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper's central claim is that support mismatch from a charged local operator is local and can be restored by a local basis rotation applied only to the sampling basis, leaving the variational wavefunction and projector unchanged. This is presented via explicit construction of the rotation scheme, with benchmarks against exact results in 1D and 2D. No equations reduce any result to a fitted parameter renamed as prediction, no self-citation chain is load-bearing for the locality argument, and the method is an independent modification to sampling without self-definitional loops or ansatz smuggling. The derivation is self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The proposal rests on standard variational Monte Carlo sampling assumptions and the locality of the support mismatch; no free parameters or new entities are introduced in the abstract.

axioms (1)
  • domain assumption Standard assumptions of variational Monte Carlo sampling and projective dynamics
    The method extends existing VMC framework without stating new axioms.

pith-pipeline@v0.9.1-grok · 5737 in / 1105 out tokens · 28946 ms · 2026-06-26T06:24:40.977931+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

65 extracted references · 1 canonical work pages

  1. [1]

    Carleo, F

    G. Carleo, F. Becca, M. Schir` o, and M. Fabrizio, Lo- calization and glassy dynamics of many-body quantum systems, Sci. Rep.2, 243 (2012)

    2012

  2. [2]

    Carleo, F

    G. Carleo, F. Becca, L. Sanchez-Palencia, S. Sorella, and M. Fabrizio, Light-cone effect and supersonic correlations in one- and two-dimensional bosonic superfluids, Phys. Rev. A89, 031602 (2014)

    2014

  3. [3]

    Wu and J

    Y. Wu and J. Nys, Real-time dynamics in two dimen- sions with tensor network states via time-dependent variational monte carlo (2026), arXiv:2512.06768 [cond- mat.str-el]

    arXiv 2026

  4. [4]

    Carleo and M

    G. Carleo and M. Troyer, Solving the quantum many- body problem with artificial neural networks, Science 355, 602 (2017)

    2017

  5. [5]

    J. Nys, Z. Denis, and G. Carleo, Real-time quantum dy- namics of thermal states with neural thermofields, Phys. Rev. B109, 235120 (2024)

    2024

  6. [6]

    Mendes-Santos, M

    T. Mendes-Santos, M. Schmitt, and M. Heyl, Highly re- solved spectral functions of two-dimensional systems with neural quantum states, Phys. Rev. Lett.131, 046501 (2023)

    2023

  7. [7]

    Schmitt and M

    M. Schmitt and M. Heyl, Quantum many-body dynamics in two dimensions with artificial neural networks, Phys. Rev. Lett.125, 100503 (2020)

    2020

  8. [8]

    Medvidovi´ c and D

    M. Medvidovi´ c and D. Sels, Variational quantum dynam- ics of two-dimensional rotor models, PRX Quantum4, 040302 (2023)

    2023

  9. [9]

    I. L. Guti´ errez and C. B. Mendl, Real time evolution with neural-network quantum states, Quantum6, 627 (2022)

    2022

  10. [10]

    Donatella, Z

    K. Donatella, Z. Denis, A. Le Boit´ e, and C. Ciuti, Dy- namics with autoregressive neural quantum states: Ap- plication to critical quench dynamics, Phys. Rev. A108, 022210 (2023)

    2023

  11. [11]

    Carleo, L

    G. Carleo, L. Cevolani, L. Sanchez-Palencia, and M. Holzmann, Unitary dynamics of strongly interacting Bose gases with the time-dependent variational Monte Carlo method in continuous space, Phys. Rev. X7, 031026 (2017)

    2017

  12. [12]

    Schmitt and M

    M. Schmitt and M. Heyl, Quantum dynamics in transverse-field Ising models from classical networks, Sci- Post Phys.4, 013 (2018)

    2018

  13. [13]

    Czischek, M

    S. Czischek, M. G¨ arttner, and T. Gasenzer, Quenches near Ising quantum criticality as a challenge for artificial neural networks, Phys. Rev. B98, 024311 (2018)

    2018

  14. [14]

    Verdel, M

    R. Verdel, M. Schmitt, Y.-P. Huang, P. Karpov, and M. Heyl, Variational classical networks for dynamics in interacting quantum matter, Phys. Rev. B103, 165103 (2021)

    2021

  15. [15]

    Burau and M

    H. Burau and M. Heyl, Unitary long-time evolution with quantum renormalization groups and artificial neural networks, Phys. Rev. Lett.127, 050601 (2021)

    2021

  16. [16]

    Lin and F

    S.-H. Lin and F. Pollmann, Scaling of neural-network quantum states for time evolution, Phys. Status Solidi B259, 2100172 (2022)

    2022

  17. [17]

    Hofmann, G

    D. Hofmann, G. Fabiani, J. H. Mentink, G. Carleo, and M. A. Sentef, Role of stochastic noise and generalization error in the time propagation of neural-network quantum states, SciPost Phys.12, 165 (2022)

    2022

  18. [18]

    Van de Walle, M

    A. Van de Walle, M. Schmitt, and A. Bohrdt, Many-body dynamics with explicitly time-dependent neural quantum states, Mach. Learn.: Sci. Technol.6, 045011 (2025)

    2025

  19. [19]

    M. J. Hartmann and G. Carleo, Neural-network approach to dissipative quantum many-body dynamics, Phys. Rev. Lett.122, 250502 (2019)

    2019

  20. [20]

    Nagy and V

    A. Nagy and V. Savona, Variational quantum Monte Carlo method with a neural-network ansatz for open quantum systems, Phys. Rev. Lett.122, 250501 (2019)

    2019

  21. [21]

    M. Reh, M. Schmitt, and M. G¨ arttner, Time-dependent variational principle for open quantum systems with ar- tificial neural networks, Phys. Rev. Lett.127, 230501 (2021)

    2021

  22. [22]

    Haegeman, J

    J. Haegeman, J. I. Cirac, T. J. Osborne, I. Piˇ zorn, H. Ver- schelde, and F. Verstraete, Time-dependent variational principle for quantum lattices, Phys. Rev. Lett.107, 070601 (2011)

    2011

  23. [23]

    Sorella, Green function monte carlo with stochastic reconfiguration, Phys

    S. Sorella, Green function monte carlo with stochastic reconfiguration, Phys. Rev. Lett.80, 4558 (1998)

    1998

  24. [24]

    Sorella, Generalized lanczos algorithm for variational quantum monte carlo, Phys

    S. Sorella, Generalized lanczos algorithm for variational quantum monte carlo, Phys. Rev. B64, 024512 (2001)

    2001

  25. [25]

    Sorella, Wave function optimization in the variational monte carlo method, Phys

    S. Sorella, Wave function optimization in the variational monte carlo method, Phys. Rev. B71, 241103 (2005)

    2005

  26. [26]

    Sinibaldi, C

    A. Sinibaldi, C. Giuliani, G. Carleo, and F. Vicentini, Un- biasing time-dependent variational monte carlo by pro- jected quantum evolution, Quantum7, 1131 (2023)

    2023

  27. [27]

    Z.-Q. Wan, R. Wiersema, and S. Zhang, Removing nodal and support-mismatch pathologies in variational monte carlo via blurred sampling (2026), arXiv:2603.18148 [cond-mat.str-el]

    arXiv 2026

  28. [28]

    D. M. Ceperley, Fermion nodes, Journal of Statistical Physics63, 1237 (1991)

    1991

  29. [29]

    Liang, W.-Y

    X. Liang, W.-Y. Liu, P.-Z. Lin, G.-C. Guo, Y.-S. Zhang, and L. He, Solving frustrated quantum many-particle models with convolutional neural networks, Phys. Rev. B98, 104426 (2018)

    2018

  30. [30]

    K. Choo, T. Neupert, and G. Carleo, Two-dimensional frustratedJ 1−J2 model studied with neural network quantum states, Phys. Rev. B100, 125124 (2019)

    2019

  31. [31]

    Westerhout, N

    T. Westerhout, N. Astrakhantsev, K. S. Tikhonov, M. I. Katsnelson, and A. A. Bagrov, Generalization properties of neural network approximations to frustrated magnet ground states, Nature Communications11, 1593 (2020)

    2020

  32. [32]

    A. Chen, K. Choo, N. Astrakhantsev, and T. Neupert, Neural network evolution strategy for solving quantum sign structures, Phys. Rev. Res.4, L022026 (2022)

    2022

  33. [33]

    L. L. Viteritti, R. Rende, S. Sachdev, and G. Carleo, Ap- proaching the thermodynamic limit with neural-network quantum states (2026), arXiv:2602.02665 [cond-mat.str- el]

    arXiv 2026

  34. [34]

    M. A. Nielsen and I. L. Chuang,Quantum Computa- tion and Quantum Information: 10th Anniversary Edi- tion(Cambridge University Press, 2010)

    2010

  35. [35]

    Gravina, V

    L. Gravina, V. Savona, and F. Vicentini, Neural pro- jected quantum dynamics: a systematic study, Quantum 9, 1803 (2025), arXiv:2410.10720

    arXiv 2025

  36. [36]

    Krinitsin and M

    W. Krinitsin and M. Schmitt, Time-dependent varia- tional monte carlo without bias (2026), arXiv:2605.03930 [quant-ph]

    Pith/arXiv arXiv 2026

  37. [37]

    Villa, J

    L. Villa, J. Despres, S. J. Thomson, and L. Sanchez- Palencia, Local quench spectroscopy of many-body quan- tum systems, Phys. Rev. A102, 033337 (2020)

    2020

  38. [38]

    S. R. White and I. Affleck, Spectral function for theS= 1 Heisenberg antiferromagetic chain, Phys. Rev. B77, 12 134437 (2008)

    2008

  39. [39]

    Wang and H.-Q

    L. Wang and H.-Q. Lin, Dynamic structure factor from real time evolution and exact correction vectors with matrix product states (2019), arXiv:1901.07751 [cond- mat.str-el]

    Pith/arXiv arXiv 2019

  40. [40]

    Ferrari and F

    F. Ferrari and F. Becca, Spectral signatures of fractional- ization in the frustrated heisenberg model on the square lattice, Phys. Rev. B98, 100405 (2018)

    2018

  41. [41]

    Hangleiter, I

    D. Hangleiter, I. Roth, D. Nagaj, and J. Eis- ert, Easing the monte carlo sign prob- lem, Science Advances6, eabb8341 (2020), https://www.science.org/doi/pdf/10.1126/sciadv.abb8341

    work page doi:10.1126/sciadv.abb8341 2020

  42. [42]

    A. J. Kim, P. Werner, and R. Valent´ ı, Alleviating the sign problem in quantum monte carlo simulations of spin- orbit-coupled multiorbital hubbard models, Phys. Rev. B 101, 045108 (2020)

    2020

  43. [43]

    X. Qian, J. Huang, and M. Qin, Augmenting density ma- trix renormalization group with clifford circuits, Phys. Rev. Lett.133, 190402 (2024)

    2024

  44. [44]

    X. Qian, J. Huang, and M. Qin, Clifford circuits aug- mented time-dependent variational principle, Phys. Rev. Lett.134, 150404 (2025)

    2025

  45. [45]

    C. Fan, X. Qian, H.-C. Zhang, R.-Z. Huang, M. Qin, and T. Xiang, Disentangling critical quantum spin chains with clifford circuits, Phys. Rev. B111, 085121 (2025)

    2025

  46. [46]

    Elben, S

    A. Elben, S. T. Flammia, H.-Y. Huang, R. Kueng, J. Preskill, B. Vermersch, and P. Zoller, The random- ized measurement toolbox, Nature Reviews Physics5, 9 (2023)

    2023

  47. [47]

    Huang, R

    H.-Y. Huang, R. Kueng, and J. Preskill, Predicting many properties of a quantum system from very few measure- ments, Nature Physics16, 1050 (2020)

    2020

  48. [48]

    E. Lieb, T. Schultz, and D. Mattis, Two soluble models of an antiferromagnetic chain, Annals of Physics16, 407 (1961)

    1961

  49. [49]

    Jordan and E

    P. Jordan and E. Wigner, ¨Uber das paulische ¨Aquivalenzverbot, Zeitschrift f¨ ur Physik47, 631 (1928)

    1928

  50. [50]

    Perez-Garcia, F

    D. Perez-Garcia, F. Verstraete, M. M. Wolf, and J. I. Cirac, Matrix product state representations, Quantum Info. Comput.7, 401–430 (2007)

    2007

  51. [51]

    Xiang,Density Matrix and Tensor Network Renormal- ization(Cambridge University Press, Cambridge, 2023)

    T. Xiang,Density Matrix and Tensor Network Renormal- ization(Cambridge University Press, Cambridge, 2023)

    2023

  52. [52]

    E. H. Lieb and D. W. Robinson, The finite group velocity of quantum spin systems, Communications in Mathemat- ical Physics28, 251 (1972)

    1972

  53. [53]

    Caux and J

    J.-S. Caux and J. M. Maillet, Computation of dynamical correlation functions of heisenberg chains in a magnetic field, Phys. Rev. Lett.95, 077201 (2005)

    2005

  54. [54]

    J.-S. Caux, R. Hagemans, and J. M. Maillet, Compu- tation of dynamical correlation functions of heisenberg chains: the gapless anisotropic regime, Journal of Statis- tical Mechanics: Theory and Experiment2005, P09003 (2005)

    2005

  55. [55]

    Caux, Correlation functions of integrable models: A description of the abacus algorithm, Journal of Math- ematical Physics50, 095214 (2009)

    J.-S. Caux, Correlation functions of integrable models: A description of the abacus algorithm, Journal of Math- ematical Physics50, 095214 (2009)

    2009

  56. [56]

    M¨ uller, H

    G. M¨ uller, H. Thomas, H. Beck, and J. C. Bonner, Quan- tum spin dynamics of the antiferromagnetic linear chain in zero and nonzero magnetic field, Phys. Rev. B24, 1429 (1981)

    1981

  57. [57]

    Park and M

    C.-Y. Park and M. J. Kastoryano, Geometry of learning neural quantum states, Phys. Rev. Res.2, 023232 (2020)

    2020

  58. [58]

    Misery, L

    A. Misery, L. Gravina, A. Santini, and F. Vicentini, Look- ing elsewhere: improving variational monte carlo gradi- ents by importance sampling (2025), arXiv:2507.05352 [quant-ph]

    arXiv 2025

  59. [59]

    Marshall, Antiferromagnetism, Proceedings of the Royal Society of London

    W. Marshall, Antiferromagnetism, Proceedings of the Royal Society of London. A. Mathe- matical and Physical Sciences232, 48 (1955), https://royalsocietypublishing.org/rspa/article- pdf/232/1188/48/49224/rspa.1955.0200.pdf

    arXiv 1955

  60. [60]

    C. Fan, B. Zhan, Y. Gu, T. Liu, Y. Wu, M. Qin, D. Lv, and T. Xiang, Disentangling tensor network states with deep neural network (2026), arXiv:2603.14425 [cond- mat.str-el]

    arXiv 2026

  61. [61]

    Carleo, K

    G. Carleo, K. Choo, D. Hofmann, J. E. Smith, T. Wester- hout, F. Alet, E. J. Davis, S. Efthymiou, I. Glasser, S.-H. Lin, M. Mauri, G. Mazzola, C. B. Pereira, and F. Vicen- tini, Netket: A machine learning toolkit for many-body quantum systems, SoftwareX10, 100311 (2019)

    2019

  62. [62]

    Vicentini, D

    F. Vicentini, D. Hofmann, A. Szab´ o, D. Wu, C. Roth, C. Giuliani, G. Pescia, J. Nys, V. Vargas-Calder´ on, N. Astrakhantsev, and G. Carleo, Netket 3: Machine learning toolbox for many-body quantum systems, Sci- Post Phys. Codebases , 7 (2022)

    2022

  63. [63]

    Gravina and F

    L. Gravina and F. Vicentini, ptvmc-systematic-study package (2025)

    2025

  64. [64]

    J. C. Butcher,Numerical Methods for Ordinary Differ- ential Equations, 3rd ed. (John Wiley & Sons, 2016)

    2016

  65. [65]

    W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery,Numerical Recipes 3rd Edition: The Art of Sci- entific Computing(Cambridge University Press, 2007)

    2007