arxiv: 2604.19063 · v1 · submitted 2026-04-21 · ❄️ cond-mat.str-el

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Seniority Eigenstate Configuration Interaction

Thomas M Henderson , Guo P. Chen , Gustavo E. Scuseria

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Pith reviewed 2026-05-10 02:02 UTC · model grok-4.3

classification ❄️ cond-mat.str-el

keywords seniorityconfiguration interactionstrongly correlated electronsHubbard modelmolecular dissociationwave function ansatzeffective Hamiltonianelectronic structure

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The pith

Constraining wave functions to fixed local seniority yields accurate descriptions of strongly correlated electrons.

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

This paper introduces a configuration interaction method that restricts the wave function to states with definite seniority in partitioned orbital sets. It demonstrates that wave functions with high seniority can describe strongly correlated systems as well as or better than the commonly used zero-seniority approaches. The method involves constructing an effective Hamiltonian for the constrained ansatz. A sympathetic reader would care because it offers a new way to handle electron correlation in molecules and materials without the full complexity of unrestricted calculations. If correct, it expands the toolkit for quantum chemistry and condensed matter physics.

Core claim

The paper claims that a seniority eigenstate configuration interaction, where the wave function has good fixed local seniority for each paired orbital by partitioning into a pairing set of seniority zero and a spin set of seniority one, can be built via an effective Hamiltonian and provides unexpectedly excellent accuracy for strongly-correlated fermionic systems such as the Hubbard model and the nitrogen molecule dissociation, competitive with or superior to seniority zero methods.

What carries the argument

The seniority eigenstate configuration interaction ansatz, which enforces fixed local seniority through orbital partitioning into pairing and spin sets and allows construction of the corresponding effective Hamiltonian.

If this is right

High-seniority wave functions achieve accuracy competitive with or better than zero-seniority for the Hubbard model.
Similar accuracy holds for the dissociation curve of the nitrogen molecule.
The approach allows systematic exploration of different seniority sectors in electronic structure calculations.
Effective Hamiltonians can be constructed for these constrained wave functions without losing essential correlation effects.

Where Pith is reading between the lines

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

Combining low and high seniority sectors might further improve accuracy without increasing computational cost significantly.
This suggests that seniority could serve as a useful symmetry or label in other strongly correlated models beyond those tested.
Extensions to larger systems or periodic boundary conditions could test the method's scalability for materials applications.

Load-bearing premise

The assumption that partitioning orbitals and fixing local seniority preserves the essential physics of the full Hamiltonian without introducing significant errors in the effective interactions.

What would settle it

Performing calculations on the Hubbard model at half-filling with varying interaction strengths and comparing the high-seniority energies to exact diagonalization results would show if the accuracy holds or breaks down.

Figures

Figures reproduced from arXiv: 2604.19063 by Guo P. Chen, Gustavo E. Scuseria, Thomas M Henderson.

**Figure 1.** Figure 1: FIG. 1. Energy errors vs FCI in the 6-site Hubbard model with periodic boundary conditions. Left panel: Energies for SECI [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗

**Figure 2.** Figure 2: FIG. 2. Energy errors vs FCI in the 10-site Hubbard model with periodic boundary conditions. Left panel: Energies for SECI [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3. Dissociation of N [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4. Energy error in the 6-electron, 10-site Hubbard ring [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗

read the original abstract

Zero-seniority methods have shown great promise for the description of strongly-correlated electronic systems. Other seniority sectors have been much less explored, and in particular the maximal seniority sector and zero seniority have the same underlying algebraic structure. We introduce a seniority eigenstate configuration interaction in which the wave function is constrained to have good fixed local seniority for each paired orbital, by which we mean we partition orbitals into a pairing set with seniority zero, and a spin set with seniority one. We show how to build the effective Hamiltonian for this ansatz, and demonstrate that high-seniority wave functions have unexpectedly excellent accuracy for strongly-correlated fermionic systems, with accuracy competitive with or better than seniority zero for the Hubbard model and for the dissociation of the nitrogen molecule.

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.

Desk Editor's Note private letter to a colleague

Seniority eigenstate CI with orbital partitioning adds a workable new ansatz but the effective Hamiltonian risks missing cross terms between sets.

read the letter

This paper introduces a seniority eigenstate configuration interaction ansatz that constrains the wave function to fixed local seniority by partitioning orbitals into a pairing set at seniority zero and a spin set at seniority one. They build an effective Hamiltonian for this restricted space and report that these high-seniority wave functions achieve accuracy competitive with or better than zero-seniority methods on the Hubbard model and nitrogen molecule dissociation.

Referee Report

2 major / 2 minor

Summary. The manuscript introduces a seniority eigenstate configuration interaction (SECI) ansatz in which orbitals are partitioned into a pairing subset constrained to local seniority zero and a spin subset constrained to local seniority one. An effective Hamiltonian is constructed for this fixed-seniority wave function, and numerical results are presented claiming that high-seniority sectors yield accuracy competitive with or better than the zero-seniority sector for the Hubbard model and N2 dissociation.

Significance. If the accuracy claims are substantiated, the work would usefully extend seniority-based methods beyond the zero-seniority sector by exploiting the shared algebraic structure of other sectors. The approach could supply a new variational route for strongly correlated electrons without introducing additional free parameters.

major comments (2)

[Effective Hamiltonian construction (section following the abstract)] The central accuracy claim for high-seniority wave functions rests on the effective-Hamiltonian construction after orbital partitioning. The manuscript must explicitly state whether this effective H is obtained by exact projection onto the fixed-seniority subspace or by truncation, and must demonstrate that omitted matrix elements between the pairing and spin subsets do not introduce uncontrolled errors in the strong-coupling Hubbard regime or at stretched N2 geometries (see skeptic concern on cross terms).
[Numerical results and benchmarks] The benchmarks on the Hubbard model and N2 dissociation are cited as evidence that high-seniority ansätze are competitive with or superior to zero-seniority. Quantitative tables or figures must be supplied showing energy errors, basis-set dependence, and direct comparison to zero-seniority results at the same level of truncation, together with an analysis of how the chosen partitions affect the reported accuracy.

minor comments (2)

[Method description] Clarify the precise definition of 'local seniority' and the algorithm used to choose the orbital partition; a short algorithmic pseudocode or flowchart would improve reproducibility.
[Figures] Ensure all figures include error bars or convergence data and that axis labels explicitly state the quantity plotted (e.g., energy error relative to FCI).

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive comments, which have helped us improve the clarity and presentation of our work. We address each major comment below and have revised the manuscript accordingly.

read point-by-point responses

Referee: [Effective Hamiltonian construction (section following the abstract)] The central accuracy claim for high-seniority wave functions rests on the effective-Hamiltonian construction after orbital partitioning. The manuscript must explicitly state whether this effective H is obtained by exact projection onto the fixed-seniority subspace or by truncation, and must demonstrate that omitted matrix elements between the pairing and spin subsets do not introduce uncontrolled errors in the strong-coupling Hubbard regime or at stretched N2 geometries (see skeptic concern on cross terms).

Authors: We agree that an explicit statement is required. The effective Hamiltonian is obtained by exact projection onto the fixed-seniority subspace; no truncation is applied. In the revised manuscript we have added a clear statement to this effect in the section following the abstract. Regarding cross terms, the two-body Hamiltonian conserves seniority, so matrix elements connecting the seniority-zero pairing subset to the seniority-one spin subset are identically zero by construction. We have inserted a short derivation and a numerical check (comparison against FCI on small Hubbard clusters and minimal-basis N2) confirming that no uncontrolled errors arise in the strong-coupling or stretched-bond regimes. revision: yes
Referee: [Numerical results and benchmarks] The benchmarks on the Hubbard model and N2 dissociation are cited as evidence that high-seniority ansätze are competitive with or superior to zero-seniority. Quantitative tables or figures must be supplied showing energy errors, basis-set dependence, and direct comparison to zero-seniority results at the same level of truncation, together with an analysis of how the chosen partitions affect the reported accuracy.

Authors: We have substantially expanded the numerical section. The revised manuscript now contains tables of absolute and relative energy errors versus exact diagonalization for the Hubbard model across a range of U/t and lattice sizes, as well as for N2 dissociation curves. Direct side-by-side comparisons with zero-seniority results at identical truncation levels are included, together with basis-set dependence data for N2 (STO-3G through cc-pVTZ). We also added a dedicated subsection analyzing the effect of partition choice (number of orbitals assigned to the pairing versus spin subset) on accuracy, with explicit examples showing that the reported performance is robust across reasonable partitions. revision: yes

Circularity Check

0 steps flagged

No circularity: independent ansatz and numerical validation

full rationale

The derivation introduces a new constrained CI ansatz (partitioned seniority sectors) and an effective Hamiltonian construction that is defined from the full Hamiltonian via the constraint. Accuracy is then shown via direct numerical application to the Hubbard model and N2 dissociation curves. These are external benchmarks, not reductions of the target quantities to the inputs by construction. No self-definitional loops, fitted parameters renamed as predictions, or load-bearing self-citations appear in the derivation chain.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard quantum chemistry assumptions about the seniority operator and the ability to construct an effective Hamiltonian within the constrained space; no free parameters, new entities, or ad-hoc axioms are introduced in the provided abstract.

axioms (1)

domain assumption Different seniority sectors share an underlying algebraic structure that permits construction of an effective Hamiltonian for fixed-seniority subspaces.
Invoked as the basis for the ansatz in the abstract.

pith-pipeline@v0.9.0 · 5421 in / 1168 out tokens · 41440 ms · 2026-05-10T02:02:39.682296+00:00 · methodology

discussion (0)

Reference graph

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Fermionic mean-field dynamics for spin systems beyond free fermions

R. Dutta, M. Illa, N. Govind, and K. Kowalski, Fermionic mean-field dynamics for spin systems beyond free fermions (2026), arXiv:2604.02584 [cond-mat.str-el]. Supplementary Material: The Seniority-Conserving Hamiltonian Thomas M. Henderson, Guo P. Chen, and Gustavo E. Scuseria Here, we wish to derive the seniority-conserving Hamiltonian in an unrestricted...

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