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arxiv: 2606.30585 · v1 · pith:Y3LPI23Mnew · submitted 2026-06-29 · ❄️ cond-mat.mtrl-sci

Excitons in Large Disordered Boron-Nitride Layer using Linear-Scaling Bethe-Salpeter Simulations

Thomas Galvani , Lorenzo Sponza , Hakim Amara , Sylvain Latil , Stephan Roche This is my paper

Pith reviewed 2026-06-30 04:41 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci
keywords excitonsboron nitrideBethe-Salpeter equationlinear scalingdisorderAnderson localizationoptical absorptiontwo-dimensional materials
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The pith

A real-space linear-scaling Bethe-Salpeter method computes excitonic spectra in disordered boron-nitride systems with up to 100,000 orbitals.

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

The paper introduces a computational framework that makes excitonic calculations feasible for large, disordered layers of boron nitride. It relies on a perturbative mapping of electron-hole pairs onto a sparse tight-binding model followed by the kernel polynomial method to reach linear scaling with system size. This enables simulations of systems far beyond the reach of standard Green's function approaches. The authors apply the method to Anderson-disordered hexagonal boron nitride and report how disorder alters exciton broadening, peak shifts, and spatial localization. The work matters because it extends optical spectroscopy to moiré, quasicrystalline, and other structurally complex materials.

Core claim

A sublattice-resolved perturbative decoupling maps localized electron-hole pairs onto a sparse tight-binding model, allowing the kernel polynomial method to evaluate absorption spectra at O(N) cost within a real-space Bethe-Salpeter framework; when applied to Anderson-disordered monolayer hexagonal boron nitride containing up to 10^5 orbitals, the calculations show disorder-induced asymmetric broadening of bright excitons, a quadratic-to-linear crossover in the redshift of the main peak, and Anderson localization of the exciton center of mass.

What carries the argument

Sublattice-resolved perturbative decoupling that maps localized electron-hole pairs onto a sparse tight-binding model, combined with the kernel polynomial method to achieve linear-scaling spectra.

If this is right

  • Excitonic spectroscopy becomes accessible for systems containing 10^5 orbitals or more.
  • Disorder produces asymmetric broadening of bright excitons together with a crossover from quadratic to linear redshift of the main absorption peak.
  • The exciton center of mass undergoes Anderson localization under increasing disorder strength.
  • Optical properties can be studied in moiré, quasicrystalline, and structurally complex quantum materials.

Where Pith is reading between the lines

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

  • The same linear-scaling strategy could be transferred to other two-dimensional materials that exhibit localized excitons.
  • Predictions of exciton localization may guide design of disordered optoelectronic devices based on boron-nitride layers.
  • Extensions that incorporate finite temperature or external electric fields would follow naturally from the existing O(N) machinery.
  • Systematic benchmarking against conventional GW-BSE results on progressively larger ordered clusters would quantify the mapping error.

Load-bearing premise

The sublattice-resolved perturbative decoupling accurately maps localized electron-hole pairs onto the sparse tight-binding model without introducing significant errors for the disordered systems studied.

What would settle it

Direct numerical comparison of absorption spectra or exciton localization lengths obtained from the linear-scaling method against exact diagonalization results on the same small disordered clusters.

Figures

Figures reproduced from arXiv: 2606.30585 by Hakim Amara, Lorenzo Sponza, Stephan Roche, Sylvain Latil, Thomas Galvani.

Figure 1
Figure 1. Figure 1: Main panel: Calculated optical response E 2 ε2(E), normalized to 1/3 of the main pristine excitonic peak, for different Anderson disorder strengths. Inset: color map of the same as a function of photon energy and disorder strength, superimposed with main peak position and fits of its disorder-induced shift. Anderson disorder, which could mimic spatial en￾ergy variations of onsite potential due to environ￾m… view at source ↗
Figure 3
Figure 3. Figure 3: a depicts ρ e Ψ(n) − ρ h Ψ(p) for the lowest bound excitonic eigenspace in a supercell made of only 578 atoms.28,29 Here, one disorder realization {ϵn}n was fixed and only scaled up with W0 for consistency. While at W0 = 0 we recover the expected Bloch states [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
read the original abstract

We introduce a real-space, linear-scaling Bethe-Salpeter framework that enables excitonic spectroscopy in large and possibly disordered boron-nitride-derived systems. Thanks to the use of a sublattice-resolved perturbative decoupling that maps localized electron-hole pairs onto a sparse tight-binding model, we implement the Kernel Polynomial Method to compute absorption spectra with O(N) cost. To illustrate the capabilities of our method, we apply it to Anderson-disordered monolayer hexagonal boron nitride with up to $10^{5}$ orbitals. The method reveals a disorder-induced asymmetric broadening of bright excitons, a crossover from quadratic to linear redshift of the main absorption peak, and Anderson localization of the exciton center of mass. This approach extends excitonic calculations beyond the reach of conventional ab initio Green's function methods (GW approximation and Bethe-Salpeter equation), opening optical spectroscopy to large-scale, disordered, moir\'e, quasicrystalline, and structurally complex quantum materials.

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

1 major / 0 minor

Summary. The paper introduces a real-space linear-scaling Bethe-Salpeter framework for excitonic spectroscopy in large and disordered boron-nitride systems. It employs a sublattice-resolved perturbative decoupling to map localized electron-hole pairs onto a sparse tight-binding model, enabling the kernel polynomial method for O(N) absorption spectra. The approach is demonstrated on Anderson-disordered monolayer hBN with up to 10^5 orbitals, reporting asymmetric broadening of bright excitons, a quadratic-to-linear crossover in the redshift of the main peak, and Anderson localization of the exciton center of mass. This extends conventional GW+BSE methods to previously inaccessible scales.

Significance. If the central approximation holds with controlled accuracy, the work would enable first-principles excitonic calculations in large disordered, moiré, and structurally complex materials, a capability currently limited by the cubic or worse scaling of standard BSE implementations. The reported physical effects on exciton broadening, redshift, and localization in disordered hBN illustrate the method's potential to generate new, testable predictions in materials science.

major comments (1)
  1. [Abstract / method description of the sublattice-resolved perturbative decoupling] Abstract and method description of the sublattice-resolved perturbative decoupling: the central claim that this decoupling maps localized e-h pairs onto a sparse TB model without significant errors for Anderson-disordered systems (up to 10^5 orbitals) is load-bearing for all reported spectra and phenomena, yet the manuscript provides no controlled error estimate, convergence test with respect to disorder strength, or direct comparison to dense BSE on the same small disordered realizations.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading and constructive feedback on our manuscript. The major comment raises a valid point about validation of the central approximation. We address it point-by-point below and will incorporate the requested material in a revised version.

read point-by-point responses

  1. Referee: Abstract and method description of the sublattice-resolved perturbative decoupling: the central claim that this decoupling maps localized e-h pairs onto a sparse TB model without significant errors for Anderson-disordered systems (up to 10^5 orbitals) is load-bearing for all reported spectra and phenomena, yet the manuscript provides no controlled error estimate, convergence test with respect to disorder strength, or direct comparison to dense BSE on the same small disordered realizations.

    Authors: We agree that controlled validation of the sublattice-resolved perturbative decoupling is important. The manuscript focuses on demonstrating O(N) scaling for systems where dense BSE is infeasible, but we acknowledge the absence of direct benchmarks. In the revised manuscript we will add a dedicated validation section comparing the approximate spectra and exciton properties against dense BSE on the same small Anderson-disordered hBN realizations (up to several hundred orbitals) for a range of disorder strengths. This will include quantitative error estimates on peak positions, broadening, and oscillator strengths, as well as tests of convergence with disorder strength. These additions will directly address the load-bearing nature of the approximation. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper presents a new real-space linear-scaling BSE framework based on sublattice-resolved perturbative decoupling mapped to a sparse TB model followed by KPM for spectra. No equations or claims in the provided text reduce results to self-definitions, fitted inputs renamed as predictions, or load-bearing self-citations that collapse the central result. The method is framed as an extension enabling new applications, with independent content in the implementation for disordered systems up to 10^5 orbitals. This is the expected self-contained case for a methods paper.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract provides no explicit free parameters, axioms, or invented entities; insufficient detail to populate ledger entries.

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discussion (0)

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Reference graph

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