arxiv: 2605.05064 · v1 · submitted 2026-05-06 · ❄️ cond-mat.str-el · cond-mat.mes-hall· physics.comp-ph

Recognition: unknown

Interaction-controlled localization in one-dimensional chain: From edges to domain walls

Rahul Samanta , Sudin Ganguly , Santanu K. Maiti

Authors on Pith no claims yet

Pith reviewed 2026-05-08 16:30 UTC · model grok-4.3

classification ❄️ cond-mat.str-el cond-mat.mes-hallphysics.comp-ph

keywords Su-Schrieffer-Heeger chainextended Hubbard modeledge modesdomain wallslocalizationHartree-Fockspin-density wavecharge-density wave

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The pith

In the interacting SSH chain, the ratio 2V/U switches bound-state localization from edge spin-density waves to mid-chain charge-density-wave domain walls.

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

The paper uses Hartree-Fock mean-field theory to examine how on-site repulsion U and nearest-neighbor repulsion V affect localized states in a half-filled Su-Schrieffer-Heeger chain. It finds that the location and type of these states are set by the single ratio 2V/U, not by whether the underlying band structure is topological, critical, or trivial. When U exceeds 2V, spin-density-wave modes appear at the chain ends; when V exceeds U/2, charge-density-wave domain walls form in the interior. This establishes that interactions alone can create and relocate bound states in finite one-dimensional chains.

Core claim

The localization of bound states is controlled by the ratio 2V/U, with edge spin-density-wave modes for U>2V and mid-chain charge-density-wave domain walls for U<2V, independent of band topology. These results establish the correlation-driven origin of localized states in finite one-dimensional chains.

What carries the argument

The dimensionless ratio 2V/U that selects between edge spin-density-wave localization and interior charge-density-wave domain walls under Hartree-Fock decoupling of the extended Hubbard model on the SSH lattice.

If this is right

Localized states can be moved from the edges to the chain interior simply by increasing the relative strength of extended repulsion V.
Band topology loses its control over localization site once interactions are turned on.
The character of the localized density changes from spin-density-wave to charge-density-wave as the ratio crosses unity.
The same interaction-controlled behavior appears in all three hopping regimes: topological, critical, and trivial.

Where Pith is reading between the lines

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

Tuning the ratio 2V/U in cold-atom or quantum-dot realizations of the SSH chain could provide a direct experimental test of interaction-driven relocation of bound states.
In the presence of strong one-dimensional fluctuations, the critical ratio at which domain walls appear may shift away from 2V/U.
Analogous ratio-controlled switches between edge and interior localization may operate in other one-dimensional interacting models that lack the SSH dimerization.

Load-bearing premise

The Hartree-Fock mean-field treatment accurately captures the localization physics without significant beyond-mean-field fluctuations or correlation effects that are known to be strong in one dimension.

What would settle it

Exact diagonalization or density-matrix renormalization group results on finite chains showing the switch between edge and mid-chain localization at a ratio clearly different from 2V/U.

Figures

Figures reproduced from arXiv: 2605.05064 by Rahul Samanta, Santanu K. Maiti, Sudin Ganguly.

**Figure 1.** Figure 1: FIG. 1: (Color online). Schematic diagram of the one view at source ↗

**Figure 2.** Figure 2: FIG. 2: (Color online). (a) Energy eigenvalue spectrum as a view at source ↗

**Figure 3.** Figure 3: FIG. 3: (Color online). (a) Energy eigenvalue spectrum as a view at source ↗

**Figure 4.** Figure 4: FIG. 4: (Color online). (a) Energy eigenvalue spectrum as a view at source ↗

**Figure 5.** Figure 5: FIG. 5: (Color online). (a) Energy eigenvalue spectrum as a view at source ↗

**Figure 6.** Figure 6: FIG. 6: (Color online). (a) Energy eigenvalue spectrum as view at source ↗

**Figure 9.** Figure 9: FIG. 9: (Color online). (a) Energy eigenvalue spectrum as view at source ↗

**Figure 8.** Figure 8: FIG. 8: (Color online). (a) Energy eigenvalue spectrum as a view at source ↗

**Figure 10.** Figure 10: FIG. 10: (Color online). Maximum left (red) and right (green view at source ↗

read the original abstract

Using Hartree-Fock mean-field approach, we study the role of on-site ($U$) and extended ($V$) Hubbard interactions on the existence and evolution of edge modes in a half-filled Su-Schrieffer-Heeger (SSH) chain. We analyze the energy spectrum, local probability amplitudes, and site-resolved charge and spin density profiles across topological, critical, and trivial hopping regimes. We find that the localization of bound states is controlled by the ratio $2V/U$, with edge spin-density-wave modes for $U>2V$ and mid-chain charge-density-wave domain walls for $U<2V$, independent of band topology. These results establish the correlation-driven origin of localized states in finite one-dimensional chains.

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

Mean-field calculation on the interacting SSH chain reports a 2V/U crossover that moves localized states from edge SDW to mid-chain CDW independent of topology, but the 1D fluctuation issue is real.

read the letter

The paper's central result is that Hartree-Fock on a half-filled SSH chain with on-site U and nearest-neighbor V produces a switch at 2V/U: when U dominates, the bound states appear as edge spin-density waves; when V dominates, they become charge-density-wave domain walls in the middle of the chain. This pattern is reported to hold across topological, critical, and trivial hopping regimes. That specific ratio and the claimed topology independence are the concrete new pieces, not just a restatement of earlier interacting-SSH work. The authors do a systematic job of scanning the three regimes, computing the spectrum, and showing the site-resolved charge and spin densities that back the localization claim. Those plots make the finding easy to visualize and test. The main limitation is the mean-field treatment. In one dimension at half filling, quantum fluctuations are strong enough that they typically suppress or smear the long-range density-wave order that Hartree-Fock assumes, turning the system into a Luttinger liquid. The paper does not compare its results to DMRG or exact diagonalization on small chains, so it is unclear whether the sharp 2V/U crossover survives once fluctuations are included. The numerics themselves look standard and reproducible from the description, with no obvious fitting or circularity. This work is mainly useful to people who already use mean-field approaches for quick scans of correlated 1D chains or who want a simple model for interaction-tuned localization. A referee could usefully check the self-consistency loop, ask for a short beyond-mean-field discussion, and verify the density profiles on a few parameter points. I would send it to peer review rather than desk-reject; the claim is specific and the calculations are transparent enough that external feedback would improve it.

Referee Report

2 major / 2 minor

Summary. The manuscript applies the Hartree-Fock mean-field approximation to a half-filled Su-Schrieffer-Heeger chain with on-site U and nearest-neighbor V interactions. It reports that the localization of bound states is governed by the ratio 2V/U, producing edge spin-density-wave modes for U>2V and mid-chain charge-density-wave domain walls for U<2V; this crossover is stated to hold independently of whether the non-interacting band structure is topological, critical, or trivial. The analysis is based on self-consistent solutions for the energy spectrum, local amplitudes, and site-resolved charge and spin densities across the three hopping regimes.

Significance. If the mean-field results are robust, the work would demonstrate a simple, interaction-tuned mechanism for relocating and recharacterizing localized states in finite 1D chains, with potential implications for correlation effects in topological wires or quantum-dot arrays. The systematic scan across topological regimes and the identification of a single control parameter (2V/U) constitute the main technical contribution.

major comments (2)

[§3] §3 (Hartree-Fock decoupling): The central claim that localization switches at 2V/U and is independent of band topology rests entirely on the Hartree-Fock site densities. In one dimension, however, quantum fluctuations are known to suppress long-range SDW/CDW order and can qualitatively alter or eliminate mean-field crossovers; the manuscript contains no comparison to DMRG, exact diagonalization, or bosonization results that would test whether the reported 2V/U threshold survives beyond mean-field.
[§4.2] §4.2 (density profiles): The edge SDW versus mid-chain CDW distinction is illustrated only via mean-field charge and spin densities. Because the Hartree-Fock ansatz assumes a product state, it cannot capture the Luttinger-liquid character or power-law correlations expected at half-filling; this directly affects the load-bearing assertion that the localization character is controlled solely by 2V/U.

minor comments (2)

[§2] The definition of the SSH hopping parameters t1 and t2 and the precise form of the interaction terms should be stated explicitly in the model section before the Hartree-Fock equations are introduced.
[Fig. 3-6] Figure captions for the density plots should include the precise values of U/V used and the system size N to allow direct reproduction.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of the manuscript and the recommendation for major revision. The comments correctly identify the mean-field character of the study and the absence of beyond-Hartree-Fock benchmarks. We respond to each point below and will incorporate clarifications in the revised version.

read point-by-point responses

Referee: [§3] §3 (Hartree-Fock decoupling): The central claim that localization switches at 2V/U and is independent of band topology rests entirely on the Hartree-Fock site densities. In one dimension, however, quantum fluctuations are known to suppress long-range SDW/CDW order and can qualitatively alter or eliminate mean-field crossovers; the manuscript contains no comparison to DMRG, exact diagonalization, or bosonization results that would test whether the reported 2V/U threshold survives beyond mean-field.

Authors: We agree that strong quantum fluctuations in one dimension generally suppress true long-range order and that the Hartree-Fock approximation cannot capture them. Our work is explicitly limited to the self-consistent Hartree-Fock treatment, within which the crossover at 2V/U and its independence from the non-interacting topology emerge consistently from the site densities and spectra. This mean-field picture still provides a transparent mechanism for how the relative strength of U and V relocates and recharacterizes the bound states. We will add a paragraph in the discussion section that explicitly states the mean-field limitation, references the expected suppression of order by fluctuations, and notes that DMRG or bosonization studies would be required to assess the survival of the 2V/U threshold. revision: partial
Referee: [§4.2] §4.2 (density profiles): The edge SDW versus mid-chain CDW distinction is illustrated only via mean-field charge and spin densities. Because the Hartree-Fock ansatz assumes a product state, it cannot capture the Luttinger-liquid character or power-law correlations expected at half-filling; this directly affects the load-bearing assertion that the localization character is controlled solely by 2V/U.

Authors: The Hartree-Fock ansatz is indeed a product state and therefore yields only average densities without Luttinger-liquid power-law correlations. The reported distinction between edge SDW and mid-chain CDW follows directly from the self-consistent solutions for the charge and spin profiles under the chosen decoupling. Within this framework the ratio 2V/U controls which instability dominates. We will revise the text around §4.2 to emphasize that the results are mean-field densities and to discuss briefly how the observed crossover relates to the competition between on-site and nearest-neighbor terms, while noting that a full Luttinger-liquid treatment lies outside the present scope. revision: partial

Circularity Check

0 steps flagged

No circularity: localization crossover emerges as output of Hartree-Fock computation

full rationale

The paper applies the Hartree-Fock mean-field decoupling to the interacting SSH Hamiltonian, computes the self-consistent site-resolved charge and spin densities, and reports that the bound-state localization switches character at the ratio 2V/U. This ratio is not inserted by definition or by fitting a subset of data and then relabeling the fit as a prediction; it is an observed outcome across the scanned parameter space. No self-citation is invoked to justify a uniqueness theorem or to smuggle an ansatz. The independence from band topology is likewise stated as a numerical finding obtained by repeating the same mean-field procedure in topological, critical, and trivial regimes. The derivation chain therefore remains self-contained against external benchmarks and does not reduce to its own inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the validity of the Hartree-Fock mean-field approximation for capturing interaction-driven localization in the SSH model; no free parameters are fitted to data and no new entities are introduced.

axioms (1)

domain assumption Hartree-Fock mean-field approximation sufficiently describes the ground-state and excitation properties of the interacting half-filled SSH chain.
The entire analysis of energy spectra, amplitudes, and density profiles is performed within this approximation.

pith-pipeline@v0.9.0 · 5429 in / 1332 out tokens · 54307 ms · 2026-05-08T16:30:03.681828+00:00 · methodology

discussion (0)

Reference graph

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