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arxiv: 2606.13342 · v1 · pith:ESEHPSNLnew · submitted 2026-06-11 · ❄️ cond-mat.str-el · cond-mat.supr-con

Variational Monte Carlo study of a two-orbital Hubbard model for the iron pnictides

Vito Marino , Gabriele Gatti , Massimo Capone , Luca F. Tocchio This is my paper

Pith reviewed 2026-06-27 05:32 UTC · model grok-4.3

classification ❄️ cond-mat.str-el cond-mat.supr-con
keywords two-orbital Hubbard modeliron pnictidesvariational Monte Carlos± superconductivityMott insulatororbital selectivityHubbard-Kanamori
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The pith

A two-orbital Hubbard-Kanamori model produces s± superconductivity only when half-filling is a Mott state, with no orbital selectivity.

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

The paper applies variational Monte Carlo to a two-orbital Hubbard-Kanamori Hamiltonian intended for iron pnictides and scans doping away from n=2. It finds a superconducting dome with s± symmetry that appears exclusively when the undoped system is Mott insulating. Orbital selectivity never develops in this regime. The outcome differs from earlier three-orbital calculations, which showed a wider superconducting region together with orbital selectivity, and instead resembles the single-band Hubbard model more closely.

Core claim

In the two-orbital Hubbard-Kanamori model, variational Monte Carlo finds a superconducting region with s± symmetry only when the half-filled (n=2) system lies inside the Mott phase; orbital selectivity remains absent throughout the parameter space examined. These features are qualitatively distinct from the three-orbital case, where superconductivity extends over a larger doping range and orbital selectivity appears together with it.

What carries the argument

Variational Monte Carlo sampling of a trial wave function that encodes s± superconducting correlations on the two-orbital Hubbard-Kanamori lattice.

If this is right

  • Superconductivity in this model is tied to the Mott insulating state at half filling.
  • Doping the Mott insulator yields s± pairing without orbital differentiation.
  • The two-orbital results align more closely with single-band Hubbard behavior than with multi-orbital extensions.
  • The Mott physics at n=2 is required for the appearance of superconductivity upon doping.

Where Pith is reading between the lines

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

  • Reducing the number of orbitals can suppress the orbital-selectivity mechanism seen in three-orbital studies.
  • Minimal models for iron pnictides may need to retain at least three orbitals to reproduce observed coexistence of superconductivity and orbital differentiation.
  • The absence of orbital selectivity could be tested by comparing the model's spectral functions to ARPES data on doped iron pnictides near the Mott boundary.

Load-bearing premise

The chosen variational wave function and interaction-parameter window are sufficient to locate the Mott transition and the true ground state.

What would settle it

Detection of s± superconductivity at dopings where the half-filled system is metallic, or emergence of orbital selectivity inside the superconducting phase.

Figures

Figures reproduced from arXiv: 2606.13342 by Gabriele Gatti, Luca F. Tocchio, Massimo Capone, Vito Marino.

Figure 1
Figure 1. Figure 1: FIG. 1. Upper panel: Optimal intra-orbital BCS parameters [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Upper panel: Optimal intra-orbital BCS parameters [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Square of the superconducting order parameter [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Fourier transform of the optimal BCS parameter, as [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Electronic density per orbital [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Pairing correlations at the maximal distance in [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗
read the original abstract

We study a two-orbital Hubbard-Kanamori model, which has been originally proposed for iron-based superconductors, using variational Monte Carlo. We span the nonmagnetic sector at both hole-doping and electron-doping, with respect to the half-filled case $n=2$. We report the presence of a superconductive region with a $s^{\pm}$ symmetry only when the half-filled system is in a Mott state, while orbital selectivity is absent. These results are qualitatively different from what was reported in the three-orbital Hubbard-Kanamori model, where a more extended superconductive region was observed with a concomitant development of orbital selectivity, and they are to some extent more reminiscent of the single-band Hubbard model.

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 / 1 minor

Summary. The manuscript reports a variational Monte Carlo study of the two-orbital Hubbard-Kanamori model for iron pnictides. Spanning the nonmagnetic sector at hole and electron doping away from half filling (n=2), the authors find a region of s± superconductivity that appears exclusively when the half-filled system realizes a Mott state, with no orbital selectivity. The findings are stated to differ qualitatively from the three-orbital version of the model and to resemble more closely the single-band Hubbard model.

Significance. If the central claim holds, the work indicates that s± pairing in this minimal model is tied directly to the Mott regime without requiring orbital polarization, thereby sharpening the distinction between two- and three-orbital descriptions of the iron pnictides and aligning the two-orbital case more closely with single-band physics.

major comments (2)
  1. [Methods and Results sections] The location of the Mott transition at n=2 and the subsequent emergence of the s± superconducting region are load-bearing for the central claim, yet the manuscript provides no benchmark of the variational ansatz (Gutzwiller+Jastrow or multi-orbital form) against DMFT, ED, or DMRG on the same two-orbital Kanamori Hamiltonian; without such validation the reported boundary between Mott and SC regimes cannot be confirmed.
  2. [Results] No system-size scaling, statistical error bars on the superconducting order parameter, or explicit diagnostic (double occupancy, charge gap, or momentum-resolved spectral function) is supplied for identifying either the Mott state or the s± order; this omission directly affects the robustness of the reported doping window.
minor comments (1)
  1. [Abstract] The abstract states that results are 'qualitatively different' from the three-orbital model but supplies no side-by-side table or figure comparing the extent of the SC region or the presence/absence of orbital selectivity between the two cases.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address the major comments point by point below.

read point-by-point responses

  1. Referee: [Methods and Results sections] The location of the Mott transition at n=2 and the subsequent emergence of the s± superconducting region are load-bearing for the central claim, yet the manuscript provides no benchmark of the variational ansatz (Gutzwiller+Jastrow or multi-orbital form) against DMFT, ED, or DMRG on the same two-orbital Kanamori Hamiltonian; without such validation the reported boundary between Mott and SC regimes cannot be confirmed.

    Authors: We agree that explicit benchmarks would strengthen confidence in the Mott boundary. The multi-orbital Gutzwiller-Jastrow ansatz employed here follows the form validated in earlier VMC studies of Kanamori-Hubbard models; however, direct side-by-side comparisons with DMFT, ED or DMRG on this exact two-orbital Hamiltonian are not available in the literature and would require a separate computational campaign. We will expand the Methods section with references to prior validation of the same ansatz class and a brief discussion of its expected accuracy near half filling. revision: partial

  2. Referee: [Results] No system-size scaling, statistical error bars on the superconducting order parameter, or explicit diagnostic (double occupancy, charge gap, or momentum-resolved spectral function) is supplied for identifying either the Mott state or the s± order; this omission directly affects the robustness of the reported doping window.

    Authors: We accept that the presentation would benefit from these elements. In the revised manuscript we will (i) report statistical error bars obtained from the Monte Carlo sampling on the superconducting order parameter, (ii) include a finite-size scaling analysis for the largest clusters studied, and (iii) make the diagnostics explicit by showing double occupancy versus doping and the momentum dependence of the pairing correlations that establish s± symmetry. revision: yes

Circularity Check

0 steps flagged

No significant circularity; VMC results are direct numerical outputs

full rationale

This is a variational Monte Carlo numerical study of the two-orbital Hubbard-Kanamori model. The reported s± superconducting region (present only when the half-filled system is Mott) and absence of orbital selectivity are direct outputs of the VMC energy minimization over the chosen variational wave function and parameter range. No self-definitional steps, fitted inputs renamed as predictions, or load-bearing self-citation chains appear in the abstract or description. The central claim does not reduce to its inputs by construction; the derivation is self-contained as a computational exploration.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the variational Monte Carlo method being able to locate the Mott transition and detect superconductivity, plus the assumption that the two-orbital Kanamori Hamiltonian with chosen U and J values represents iron pnictides. No new entities are postulated.

free parameters (1)
  • Hubbard U and Hund's J
    Interaction strengths in the Hubbard-Kanamori Hamiltonian are input parameters that must be chosen to place the half-filled system in or near the Mott regime.
axioms (1)
  • domain assumption Variational Monte Carlo with the chosen trial wavefunction provides a reliable estimate of the ground-state energy and order parameters.
    Standard assumption of the VMC method invoked by the choice of technique.

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