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arxiv: 2505.05883 · v2 · pith:YHATJSPEnew · submitted 2025-05-09 · ❄️ cond-mat.str-el · cond-mat.other· quant-ph

Quantum Monte Carlo description of correlated electrons in two-dimensional FeSe

S. Azadi , A. Principi , R. V. Belosludov , T. D. K\"uhne , M.S. Bahramy This is my paper

Pith reviewed 2026-05-22 16:33 UTC · model grok-4.3

classification ❄️ cond-mat.str-el cond-mat.otherquant-ph
keywords quantum Monte Carlocorrelation energyFeSedouble-layeratomic contributionstwo-dimensional materialsthermodynamic limitstrain dependence
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0 comments X

The pith

Correlation energy in double-layer FeSe is set mostly by its atoms rather than by bonds between them.

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

The paper asks how the correlation energy of atoms changes when they assemble into a double-layer FeSe solid. It computes these energies with quantum Monte Carlo for the layered material in various geometries and for separate iron and selenium atoms, then extrapolates to the thermodynamic limit. The central finding is that atomic contributions account for nearly all the correlation energy while interatomic bonding adds only a small correction. This holds even after the layer is stretched and its interlayer spacing is varied. The result matters because it shows that electron correlations in this system can be understood largely from the properties of the isolated atoms.

Core claim

Variational and diffusion quantum Monte Carlo calculations with two forms of Slater-Jastrow trial wave functions show that the correlation energy of double-layer FeSe at the thermodynamic limit is dominated by the atomic contributions; the bonding between atoms plays only a minor role. When the interlayer separation is optimized under tensile strain, the correlation energy approaches that of the constituent Fe and Se atoms as stretch and spacing increase.

What carries the argument

Direct comparison of quantum Monte Carlo correlation energies between double-layer FeSe configurations and isolated Fe and Se atoms, extrapolated to the thermodynamic limit.

If this is right

  • The correlation energy of double-layer FeSe moves closer to the atomic value as tensile strain and interlayer spacing grow.
  • Atomic contributions outweigh bonding effects in setting the total correlation energy for the structures examined.
  • Different geometrical configurations change the correlation energy but keep it close to the sum of atomic values.

Where Pith is reading between the lines

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

  • Similar atomic dominance might appear in other layered transition-metal compounds and could be checked by the same method.
  • Models that treat correlation largely at the atomic level may give useful estimates for correlation-driven properties in these materials.
  • The approach could be extended to single-layer FeSe or to doped variants to test whether the atomic picture survives changes in dimensionality or carrier density.

Load-bearing premise

The Slater-Jastrow trial wave functions and the extrapolation to the thermodynamic limit give unbiased estimates of correlation-energy differences between the double-layer system and the separate atoms.

What would settle it

A calculation with a substantially different trial wave function or a direct experimental energy measurement that finds a large bonding contribution to the correlation energy would falsify the claim.

Figures

Figures reproduced from arXiv: 2505.05883 by A. Principi, M.S. Bahramy, R. V. Belosludov, S. Azadi, T. D. K\"uhne.

Figure 1
Figure 1. Figure 1: FIG. 1. DMC correlation energy of Fe as a function of time [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: All the results of Figs. 2 and 3 were obtained [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. The difference between VMC and DFT energies as a function of the number of optimization interation. (a) Only [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. (a) VMC and (b) DMC energy of double layer FeSe [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Energy of double-layer FeSe with respect to the min [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Correlation energy per electron for double layer FeSe [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
read the original abstract

An interesting question in physics is how the correlation energy of atoms evolves upon forming a solid. Here, we address this problem for a specific case of double-layer FeSe. We used many-body wavefunction-based quantum Monte Carlo (QMC) techniques to compute the correlation energies of double-layer FeSe with different geometrical configurations and compared them with those of isolated Fe and Se atoms. Variational and diffusion QMC calculations were carried out with Slater Jastrow trial wavefunctions employing two alternative forms for the homogeneous two-body pair correlation term. The ground-state energy was obtained in the thermodynamic limit using two types of trial wave functions of JDFT, in which only the Jastrow factor is optimized while the Slater determinant is derived from the local density approximation, and JSD, where both the Jastrow factor and the Slater determinant are optimized simultaneously. Our results indicate that the correlation energy of double layer FeSe at the thermodynamic limit is mainly determined by the atomic contributions, with the bonding between atoms playing a comparatively minor role in it. After optimizing the interlayer separation of double-layer FeSe under tensile strain, we analyze the correlation energy as a function of strain and separation. We found that with increasing tensile stretch and interlayer spacing, the correlation energy of double-layer FeSe stochastically approaches that of its constituent atomic fragments.

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

2 major / 2 minor

Summary. The manuscript applies variational Monte Carlo (VMC) and diffusion Monte Carlo (DMC) with Slater-Jastrow trial wavefunctions (JDFT and JSD forms) to compute the correlation energy of double-layer FeSe. Energies are extrapolated to the thermodynamic limit and compared directly to those of isolated Fe and Se atoms. The central claim is that atomic contributions dominate the correlation energy, with interatomic bonding playing a minor role; this is further examined under tensile strain and varying interlayer separation, where the layer correlation energy is reported to approach the atomic value with increasing stretch and spacing.

Significance. If the fixed-node errors cancel as assumed, the work supplies a first-principles QMC benchmark showing that correlation in this 2D FeSe system is largely atomic rather than bonding-driven. This could constrain effective models of its electronic structure and help interpret its superconductivity. The explicit use of two trial-wavefunction forms and thermodynamic-limit extrapolation constitutes a concrete strength.

major comments (2)
  1. [§3] §3 (DMC section) and the thermodynamic-limit extrapolation paragraph: the manuscript does not demonstrate or quantify cancellation of fixed-node errors between the periodic double-layer system (whose nodes reflect band dispersion) and the isolated atoms (whose nodes reflect multiplet structure). Because the central claim rests on the solid-minus-atoms correlation-energy difference being physically meaningful rather than an artifact of unequal fixed-node penalties, this omission is load-bearing.
  2. [Results on strain] Results on strain and interlayer separation: the reported stochastic approach of the layer correlation energy to the atomic value with increasing tensile stretch is presented without error bars on the difference or a test that residual finite-size and fixed-node contributions remain smaller than the observed trend. This weakens the quantitative support for the 'minor role of bonding' conclusion.
minor comments (2)
  1. [Abstract] The abstract states the main conclusion but contains no numerical values, error estimates, or explicit comparison numbers; adding at least one representative energy difference (with uncertainty) would improve readability.
  2. [Methods] Notation for the two-body Jastrow term is introduced without an explicit functional form or reference to the precise parametrization used in the JDFT versus JSD cases.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for their careful reading and constructive comments on our manuscript. We address the major points raised below and agree that additional discussion and analysis will strengthen the presentation of our results.

read point-by-point responses

  1. Referee: [§3] §3 (DMC section) and the thermodynamic-limit extrapolation paragraph: the manuscript does not demonstrate or quantify cancellation of fixed-node errors between the periodic double-layer system (whose nodes reflect band dispersion) and the isolated atoms (whose nodes reflect multiplet structure). Because the central claim rests on the solid-minus-atoms correlation-energy difference being physically meaningful rather than an artifact of unequal fixed-node penalties, this omission is load-bearing.

    Authors: We acknowledge that the manuscript does not provide a quantitative estimate of residual fixed-node errors in the solid-atom energy difference. Our calculations use the same Slater-Jastrow forms (JDFT and JSD) for both the double-layer FeSe and the isolated atoms, and the consistency of results between these two trial wavefunctions indicates that differences in nodal surfaces do not drive the main trends. We will revise the manuscript to include an expanded discussion of the fixed-node approximation, the rationale for expecting substantial cancellation in energy differences when using consistent trial functions, and the limitations of this assumption. A rigorous numerical quantification of the cancellation, however, would require methods such as release-node DMC that are beyond the scope of the present study. revision: yes

  2. Referee: [Results on strain] Results on strain and interlayer separation: the reported stochastic approach of the layer correlation energy to the atomic value with increasing tensile stretch is presented without error bars on the difference or a test that residual finite-size and fixed-node contributions remain smaller than the observed trend. This weakens the quantitative support for the 'minor role of bonding' conclusion.

    Authors: We agree that explicit error bars on the differences and additional checks would improve the quantitative support. In the revised manuscript we will report statistical uncertainties on the correlation-energy differences, include propagated error bars in the relevant figures, and add a brief analysis comparing results across different supercell sizes and the two trial wavefunctions to confirm that finite-size and fixed-node residuals are smaller than the observed trends with strain and interlayer spacing. revision: yes

standing simulated objections not resolved
  • A complete numerical quantification of residual fixed-node errors in the solid-minus-atoms correlation energy difference.

Circularity Check

0 steps flagged

Direct first-principles QMC comparison of solid and atomic correlation energies shows no circularity

full rationale

The paper computes total energies via variational and diffusion Monte Carlo using Slater-Jastrow trial functions (JDFT with LDA-derived determinant and JSD with variationally optimized determinant) for both the double-layer FeSe supercells and the isolated Fe/Se atoms. Correlation energies are obtained from these total energies, extrapolated to the thermodynamic limit via finite-size scaling for the periodic system, and then compared numerically to quantify the difference attributable to bonding. This comparison is a direct subtraction of independently calculated quantities with no fitted parameters, no self-referential definitions of the target observable, and no load-bearing self-citations that reduce the central claim to prior inputs. The procedure is self-contained and externally falsifiable by other many-body methods.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

Relies on standard QMC assumptions for trial wavefunctions and finite-size extrapolation; no new entities postulated.

free parameters (1)
  • Jastrow factor variational parameters
    Optimized during VMC and DMC runs for both JDFT and JSD trial functions.
axioms (1)
  • domain assumption Slater determinant derived from LDA or jointly optimized suffices to capture essential correlations
    Invoked when defining the two classes of trial wavefunctions used for all energy calculations.

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Reference graph

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