arxiv: 2604.17812 · v1 · submitted 2026-04-20 · ❄️ cond-mat.supr-con · cond-mat.str-el

Recognition: unknown

Pairing properties of correlated three-leg ladders with strong interchain couplings near 1/3 filling

Yushi Yamada , Tatsuya Kaneko , Masataka Kakoi , Ryota Ueda , Kazuhiko Kuroki

Authors on Pith no claims yet

Pith reviewed 2026-05-10 04:06 UTC · model grok-4.3

classification ❄️ cond-mat.supr-con cond-mat.str-el

keywords three-leg t-J ladderpair correlationsspin gaphole dopingDMRG1/3 fillingtrilayer nickelatessuperconductivity

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The pith

In three-leg t-J ladders with strong interchain couplings, hole doping near 1/3 filling produces power-law decaying pair correlations while spin correlations decay exponentially.

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

The paper studies the ground-state properties of three-leg ladders in the t-J model with strong interchain couplings near one-third filling using density-matrix renormalization group calculations. It establishes that holes doped into the spin-gapped state at this filling give rise to dominant pairing correlations that decay as power laws, accompanied by exponentially decaying spin correlations. Electron doping into the same state does not produce comparable pairing. These results are contrasted with the Hubbard model and positioned as relevant to the electronic properties of trilayer nickelate superconductors.

Core claim

At one-third filling the three-leg t-J ladder with strong interchain couplings hosts a spin-gapped state. Upon hole doping, pair correlations develop with power-law decays while spin correlations decay exponentially. Electron doping fails to induce substantial pair correlations. The authors also examine the hole-doped regime of the corresponding three-leg Hubbard model for comparison.

What carries the argument

Density-matrix renormalization group evaluation of pair and spin correlation functions in the doped three-leg t-J ladder, which distinguishes power-law from exponential decay to identify the dominant instability.

If this is right

Pair correlations dominate over spin correlations in the hole-doped regime near 1/3 filling.
The spin sector remains gapped, as shown by the exponential decay of spin correlations.
Electron doping into the 1/3-filled state does not produce comparable pairing tendencies.
The hole-electron asymmetry may influence doping-dependent behavior in related nickelate systems.

Where Pith is reading between the lines

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

If the pairing survives in two-dimensional extensions of the model, it could indicate a microscopic route toward superconductivity in trilayer nickelates.
Analogous calculations on four-leg or wider ladders would test whether the three-leg geometry is essential for the observed pairing dominance.
The contrast with the Hubbard model implies that projecting out double occupancy is key to stabilizing the power-law pairing.

Load-bearing premise

The t-J model with strong interchain couplings and the selected parameter regime accurately represents the low-energy physics of trilayer nickelate superconductors near 1/3 filling.

What would settle it

Experimental detection of power-law pair correlations together with exponentially decaying spin correlations in a hole-doped trilayer nickelate near 1/3 filling, or the absence of such behavior in refined DMRG runs with altered interchain coupling strengths.

Figures

Figures reproduced from arXiv: 2604.17812 by Kazuhiko Kuroki, Masataka Kakoi, Ryota Ueda, Tatsuya Kaneko, Yushi Yamada.

**Figure 2.** Figure 2: FIG. 2. (a) Interchain spin correlation function [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗

**Figure 3.** Figure 3: presents the spin and pair correlation functions in the hole-doped states away from 1/3 filling. Figures 3(a) and 3(b) shows the spin correlation functions of the inner (l = 2) and outer (l = 1) chains in a semi-logarithmic plot. While the spin correlations gradually increase with hole doping, the exponentiallike decay is maintained, suggesting that the spin-singlet nature remains even with hole doping.… view at source ↗

**Figure 5.** Figure 5: FIG. 5. (a) Spin and (b) pair correlation functions in the [PITH_FULL_IMAGE:figures/full_fig_p004_5.png] view at source ↗

read the original abstract

We investigate the ground-state properties of correlated three-leg ladders near 1/3 filling. We apply the density-matrix renormalization group method to the three-leg t-J ladder with strong interchain couplings and evaluate its pairing nature. When holes are doped into the spin-gapped state at 1/3 filling, we find that pair correlations develop with power-law decays while spin correlations decay exponentially. On the other hand, doping of electrons into the 1/3-filled state does not give rise to substantial pair correlations. We also discuss the hole-doped state in the three-leg Hubbard model to compare it with the pairing state in the t-J model. Our numerical demonstrations provide insights into the electronic properties of trilayer nickelate superconductors.

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

DMRG on three-leg t-J ladders finds hole doping at 1/3 filling yields power-law pair correlations with gapped spins, unlike electron doping, but convergence details are thin.

read the letter

The main takeaway is that hole doping into the 1/3-filled spin-gapped state of a three-leg t-J ladder with strong interchain couplings leads to power-law decaying pair correlations, while spin correlations decay exponentially. Electron doping does not produce substantial pairing. This work does a good job extending DMRG studies to this specific geometry and filling, with a direct hole-versus-electron comparison that could be relevant for trilayer nickelates. Including the Hubbard model comparison for the hole-doped case adds some value by showing consistency or differences. The numerics are direct outputs from the model, with no circular definitions or fitted parameters generating the claims. The main concern is whether the power-law versus exponential distinction is robust. DMRG on finite ladders can show apparent power laws that are actually slow exponential decays if the correlation length is long compared to system size or if bond dimension is insufficient. The available information does not include explicit scaling with bond dimension or length, or the actual exponent values, so the central claim needs stronger support to be fully convincing. The paper engages straightforwardly with the literature on ladder models and nickelate materials. This is for researchers focused on numerical simulations of quasi-one-dimensional superconductors or the physics of nickelates. A reader interested in those areas would get concrete insights from the parameter choices and the doping asymmetry. It deserves peer review because it addresses an active area with appropriate methods, even if it will likely require revisions for more detailed convergence analysis.

Referee Report

2 major / 2 minor

Summary. The manuscript uses DMRG to study the three-leg t-J ladder (and, for comparison, the Hubbard model) with strong interchain couplings near 1/3 filling. It reports that hole doping away from the spin-gapped 1/3-filled state produces pair correlations that decay as a power law while spin correlations decay exponentially; electron doping yields no substantial pairing. These findings are presented as providing insight into the low-energy physics of trilayer nickelate superconductors.

Significance. If the reported distinction between power-law pairing and gapped spin correlations survives rigorous convergence checks, the work would supply concrete numerical evidence for pairing tendencies in a doped spin-gapped quasi-1D system, directly relevant to the ongoing discussion of superconductivity in trilayer nickelates. The hole-versus-electron doping asymmetry is a potentially falsifiable prediction.

major comments (2)

[Numerical results / DMRG analysis] The central claim (power-law pair correlations versus exponential spin decay upon hole doping) is stated in the abstract and elaborated in the numerical results, yet no quantitative pair exponent, spin correlation length, finite-size scaling data (e.g., L = 24 to 72), bond-dimension convergence (e.g., chi = 1000 to 4000), or truncation-error estimates are provided. Without these, the asymptotic classification cannot be distinguished from finite-size or truncation artifacts in DMRG.
[Model comparison section] The comparison between the t-J and Hubbard models is used to argue that the pairing state is robust, but the manuscript does not quantify how the effective parameters (t, J, interchain couplings) map between the two models or demonstrate that the observed power-law behavior persists under modest variations of the interchain coupling strength.

minor comments (2)

[Abstract] The abstract refers to 'power-law decays' without quoting the fitted exponent or the fitting window, which would help readers assess the quality of the power-law claim.
[Figures] Figure captions and axis labels for the correlation plots should explicitly state the system length L and bond dimension chi used for each data set.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the positive evaluation of its potential significance. The comments identify areas where additional details will improve the presentation of our DMRG results. We respond to each major comment below and have revised the manuscript accordingly.

read point-by-point responses

Referee: [Numerical results / DMRG analysis] The central claim (power-law pair correlations versus exponential spin decay upon hole doping) is stated in the abstract and elaborated in the numerical results, yet no quantitative pair exponent, spin correlation length, finite-size scaling data (e.g., L = 24 to 72), bond-dimension convergence (e.g., chi = 1000 to 4000), or truncation-error estimates are provided. Without these, the asymptotic classification cannot be distinguished from finite-size or truncation artifacts in DMRG.

Authors: We agree that explicit quantitative measures and convergence diagnostics are necessary to firmly establish the asymptotic behavior. The original figures display correlation functions for several system sizes, but we did not report fitted exponents, correlation lengths, or detailed truncation and bond-dimension data. In the revised manuscript we have added a new subsection on numerical methods and convergence. It includes finite-size scaling for L up to 72, bond-dimension sweeps, truncation-error estimates, and extracted pair-correlation exponents together with spin correlation lengths. These additions confirm that the power-law pairing and exponential spin decay are not finite-size or truncation artifacts. revision: yes
Referee: [Model comparison section] The comparison between the t-J and Hubbard models is used to argue that the pairing state is robust, but the manuscript does not quantify how the effective parameters (t, J, interchain couplings) map between the two models or demonstrate that the observed power-law behavior persists under modest variations of the interchain coupling strength.

Authors: The referee correctly observes that the original text does not provide an explicit parameter mapping or tests of interchain-coupling variations. The t-J model is introduced as the strong-coupling limit of the Hubbard model, but this correspondence was not quantified. In the revised manuscript we have expanded the model-comparison section to state the parameter correspondence (J/t derived from the Hubbard U) and to present additional DMRG data for interchain couplings varied by approximately 20 percent around the nominal value. These calculations show that the power-law decay of pair correlations remains stable, supporting the robustness of the reported pairing state. revision: yes

Circularity Check

0 steps flagged

No significant circularity: central claims are direct DMRG outputs

full rationale

The paper's core results—power-law pair correlations and exponential spin decay upon hole doping away from the 1/3-filled spin-gapped state—are obtained as direct numerical outputs from DMRG simulations on the three-leg t-J ladder Hamiltonian. No parameters are fitted to subsets of the target data and then relabeled as predictions; no self-definitional loops exist in the correlation functions; and no load-bearing uniqueness theorems or ansatzes are imported via self-citation. The derivation chain consists of model definition, numerical method application, and measurement of correlation functions, all of which remain independent of the reported asymptotic behaviors. The comparison to the Hubbard model is likewise a separate numerical run. This is the standard, non-circular structure for a computational condensed-matter study.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the standard domain assumption that the t-J Hamiltonian with strong interchain coupling captures the essential physics of the target materials; no additional free parameters or invented entities are introduced in the abstract.

axioms (1)

domain assumption The t-J model is an appropriate effective low-energy description for the strongly correlated electrons in three-leg ladders near 1/3 filling.
Invoked by the choice of Hamiltonian for the DMRG calculations.

pith-pipeline@v0.9.0 · 5440 in / 1263 out tokens · 38617 ms · 2026-05-10T04:06:53.236210+00:00 · methodology

discussion (0)

Reference graph

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