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Autoregressive neural Slater-Jastrow ansatz for variational Monte Carlo simulation

by Stephan Humeniuk, Yuan Wan, Lei Wang

This Submission thread is now published as

Submission summary

Authors (as registered SciPost users): Stephan Humeniuk
Submission information
Preprint Link:  (pdf)
Code repository:
Date accepted: 2023-04-18
Date submitted: 2023-03-15 02:38
Submitted by: Humeniuk, Stephan
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Computational
Approaches: Theoretical, Computational


Direct sampling from a Slater determinant is combined with an autoregressive deep neural network as a Jastrow factor into a fully autoregressive Slater-Jastrow ansatz for variational quantum Monte Carlo, which allows for uncorrelated sampling. The elimination of the autocorrelation time leads to a stochastic algorithm with provable cubic scaling (with a potentially large prefactor), i.e. the number of operations for producing an uncorrelated sample and for calculating the local energy scales like $\mathcal{O}(N_s^3)$ with the number of orbitals $N_s$. The implementation is benchmarked on the two-dimensional $t-V$ model of spinless fermions on the square lattice.

Author comments upon resubmission

We thank both referees for their comments on our manuscript. The main criticisms from both referees
was lack of sufficient benchmark results and comparison with other variational methods. We have addressed this point by extending the benchmark section and the conclusion and hope that our manuscript is now ready for publication.
A list of changes is given below.

List of changes

(i) Extended benchmark section and comparison with different variants of Slater-Jastrow-RBM as published in the variational benchmark [Varbench]( and with continuous-time QMC.
(ii) Inclusion of Hartree-Fock energies for assessing correlation energies.
(iii) The effectiveness of the cooptimization of orbitals has been assessed by starting from a non-converged (i.e. non-self-consistent) Hartree-Fock Slater determinant . The variational ground state is reached even with such a poor starting point. At variance with a statement in a previous version of the paper, cooptimization is not crucially important if the Slater determinant is taken to be a fully converged Hartree-Fock solution.
(iv) The conclusion emphasizes the limitations of the current implementation, which has proof of principle character.
(v) Explanation of dashed and dotted lines in Fig. 15.

Published as SciPost Phys. 14, 171 (2023)

Reports on this Submission

Anonymous Report 2 on 2023-4-2 (Invited Report)


I am satisfied with the revised version submitted by the authors. The paper can now be accepted for publication in SciPost.

  • validity: -
  • significance: -
  • originality: -
  • clarity: -
  • formatting: -
  • grammar: -

Anonymous Report 1 on 2023-3-26 (Invited Report)


- Detailed discussion of the algorithm
- Solid numerical results and benchmarks


The authors addressed all concerns I raised in my previous report. I thus recommend publication in SciPost Physics.

  • validity: high
  • significance: high
  • originality: high
  • clarity: good
  • formatting: excellent
  • grammar: excellent

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