Emergence of non-trivial phases in interacting non-Hermitian quasiperiodic chains with power-law hopping

Aditi Chakrabarty; Sanchayan Banerjee; Sanjoy Datta; Tapan Mishra

REVIEW 4 major objections 4 minor 64 references

Emergence of non-trivial phases in interacting non-Hermitian quasiperiodic chains with power-law hopping

T0 review · 4 major / 4 minor · reviewed 2026-08-05 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read A fully real eigenspectrum can coexist with multifractal states in an interacting non-Hermitian quasiperiodic chain, so real spectrum alone does not indicate many-body localization.

desk verdict Numerical claim that a real spectrum can coexist with multifractal many-body states in a non-Hermitian quasiperiodic chain with power-law hopping; plausible but unverifiable from the available text, and finite-size scaling is the main risk. read the letter →

arxiv 2508.14724 v1 pith:KNDBUGUS submitted 2025-08-20 cond-mat.dis-nn cond-mat.other

Aditi Chakrabarty , Sanchayan Banerjee , Tapan Mishra , Sanjoy Datta This is my paper · ORCID

classification cond-mat.dis-nncond-mat.other

keywords non-Hermitianmany-bodylocalizationquasiperiodicpotentialpower-lawhoppingmultifractalitytime-reversalsymmetryskineffectmobilityedgeexactdiagonalization

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper studies a one-dimensional chain of interacting particles moving in a quasiperiodic potential, with asymmetric hopping that decays as a power of distance—a non-Hermitian system that does not conserve probability. The authors show that the common shortcut of identifying the many-body localized phase by checking whether the energy spectrum is fully real is not reliable in this model. Instead, they find a topologically trivial intermediate phase in which the eigenstates are multifractal—neither fully delocalized nor localized—while the spectrum is real, sitting between the ergodic and the localized phases. They also find that interactions erase the mobility edges and multifractal structure that exist in the non-interacting version of the model. Finally, because of the long-range hopping, the topologically non-trivial regime under periodic boundaries does not always produce the boundary-localized skin modes expected under open boundaries.

What carries the argument

The paper's model combines (i) asymmetric hopping whose amplitude decays as a power of distance, (ii) a quasiperiodic potential, and (iii) a particle–particle interaction. The phase identification uses two complementary many-body diagnostics: the complex spacing ratio, which distinguishes real from complex spectra and ergodic from localized statistics, and the scaling of the many-body inverse participation ratio, which quantifies multifractality. The key mechanism is the competition between long-range hopping (which delocalizes and can create skin modes) and the quasiperiodic potential plus interactions (which localize and restore time-reversal symmetry); in the intermediate regime this comp

What would settle it

A larger-scale numerical study (e.g., tensor-network or density-matrix renormalization group) that measures the many-body inverse participation ratio scaling in the intermediate regime: if it approaches ergodic or localized scaling as system size grows, the intermediate phase is an artifact; likewise, computing the open-boundary density profile for the topologically non-trivial ergodic regime could reveal whether skin modes appear at larger sizes.

Watch

Extended reading notes

Core claim

The central claim is that in an interacting non-Hermitian quasiperiodic chain with asymmetric power-law hopping, the reality of the eigenspectrum is not sufficient to conclude that the system is in the non-Hermitian many-body localized (NHMBL) phase. The paper identifies an intermediate, topologically trivial regime in which the many-body eigenstates are multifractal—neither fully delocalized nor localized—while the spectrum is entirely real, thus respecting time-reversal symmetry. In this intermediate regime, interactions completely suppress the multifractal and mobility edges that are present in the non-interacting model. Additionally, the paper shows that the long-range nature of the hopp

Load-bearing premise

The classification of the intermediate phase depends on extrapolating exact-diagonalization results from short chains, so the finite-size data must faithfully represent the thermodynamic limit.

Editorial extensions

If this is right

A purely real spectrum is no longer a reliable witness for non-Hermitian many-body localization; eigenstate structure must be checked as well.
The newly identified intermediate phase with multifractal states and real spectrum is a distinct phase of interacting non-Hermitian quasiperiodic matter that any comprehensive phase diagram must include.
Interactions can destroy mobility edges in long-range non-Hermitian systems, so the non-interacting phase diagram does not survive the addition of interactions.
The non-Hermitian skin effect is not guaranteed in long-range hopping models even when the periodic-boundary spectrum is topologically non-trivial; open-boundary observables must be computed explicitly.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the intermediate multifractal phase is robust at larger sizes, analogous phases may appear in other non-Hermitian models with power-law interactions, and they could be sought in experiments with dissipative cold atoms or photonic waveguides.
The suppression of skin modes by long-range hopping suggests that transport measurements in open systems with power-law couplings will not reveal the topological character of the bulk; a direct probe of the complex winding number or the density profile may be needed instead.
The interaction-driven destruction of mobility edges could be a general mechanism: sufficiently strong interactions may erase the energy separation that produces mobility edges in single-particle spectra, so this effect may be testable in clean quasiperiodic systems.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Here's the quick take: this is a numerical exact-diagonalization paper with a nice twist—reality of the eigenspectrum does not necessarily mean the system is in the NHMBL phase. The authors report an intermediate phase with multifractal states, fully real spectrum, and trivial topology, plus two additional results (interaction destroying mobility edges and long-range hopping suppressing skin modes). If correct, that's a useful addition to the non-Hermitian quasiperiodic phase-diagram literature. The question is well motivated and they cite the relevant prior work, including Xu et al. (2021) and Peng et al. (2023, 2025) on power-law hopping and skin-effect weakening.

What's new is the specific combination: interactions + power-law hopping + non-Hermitian AAH potential. That combination hasn't been studied before, as far as the abstract and references suggest. The abstract is honest about the claims and doesn't oversell.

Now the soft spots. The version I can see stops at the introduction and references—no Hamiltonian, no parameters, no finite-size scaling, no error bar. So the reader's low soundness score is a reflection of missing evidence, not a judgment on the work. The central claims are all numerical and all depend on extrapolating from chains that are necessarily small because ED with long-range interactions is expensive. The stress-test worry is on point: power-law hopping of the form t_ij ~ |i-j|^{-σ} means the effective range grows with L, so adding a few sites changes the model more than it would for short-range hopping. A Fock-space multifractal at L=12 might be ergodic or localized at L→∞. The abstract itself says the restoration of TRS happens 'before crossing over'—the word 'crossover' is exactly the finite-size phenomenon that needs to be shown to sharpen into a phase. None of this is visible in the excerpt. It's possible that the full paper does careful scaling and the intermediate phase holds up, but I can't verify that.

One more point: the claims about interactions destroying mobility edges and about skin modes not appearing are also prone to finite-size artifacts. The interaction destruction is particularly delicate because interactions mix Fock-space sectors in ways that may not stabilize until larger L.

Bottom line: give it to a referee. The question is important enough and the combination is new enough to warrant a careful look, but the referee should push hard on the finite-size scaling and ask for the explicit model and the definitions of the observables. If the intermediate phase survives scaling, this is a solid contribution to the non-Hermitian MBL literature. If it doesn't, it's still a useful documentation of a crossover, but the abstract should say so.

Referee Report

4 major / 4 minor

Summary. The paper claims to study one-dimensional interacting non-Hermitian quasiperiodic chains with asymmetric power-law hopping. The central claims are: (i) a fully real eigenspectrum does not necessarily imply non-Hermitian many-body localization (NHMBL); (ii) there exists a topologically trivial intermediate regime with multifractal eigenstates and a real spectrum; (iii) interactions destroy the multifractal and mobility edges seen in the non-interacting counterpart; and (iv) due to long-range hopping, a topologically non-trivial ergodic phase under periodic boundary conditions does not always yield boundary-localized skin modes under open boundary conditions. The manuscript as provided contains only the abstract, the introduction, and a reference list. No model Hamiltonian, parameter definitions, numerical results, finite-size scaling analysis, or error estimates are included.

Significance. The questions addressed are timely and potentially important for the understanding of non-Hermitian many-body localization, the interplay of topology, time-reversal symmetry, and long-range hopping. If the claims are substantiated, they would challenge the common identification of a real eigenspectrum with a trivial NHMBL phase and would clarify the fate of multifractality and skin effects in interacting long-range models. The paper also frames a falsifiable prediction: interactions destroy single-particle multifractal and mobility edges in the proposed intermediate regime. However, because the visible manuscript contains no technical content, the significance is entirely conditional on evidence that is not currently available.

major comments (4)

[Entire manuscript / no model section] The paper never defines the Hamiltonian. The claims require a precise specification of the quasiperiodic potential, the non-Hermitian asymmetric hopping amplitude, the power-law exponent σ, the interaction term, and the boundary conditions. Without an explicit model, none of the reported phenomena—intermediate multifractal phase, real-spectrum region, destruction of mobility edges, or absent skin effect—can be reproduced or checked. A complete model section with the Hamiltonian and all parameter definitions is essential.
[Abstract / Results (missing)] The central claims are numerical, but the manuscript contains no data, figures, or finite-size scaling analysis. In particular, the claimed intermediate multifractal phase with a fully real spectrum is a small-system-sensitive statement. With power-law hopping, the effective range grows with system size, so a crossover at L ≲ 16 can easily be mistaken for a genuine phase. The abstract's own phrase 'before crossing over' underscores this risk. The authors must provide scaling collapse of multifractal exponents (e.g., IPR or D_q), spectral statistics, and spectral-reality fraction across several system sizes, with a clear criterion distinguishing a phase from a finite-size crossover.
[Phase classification / topology (Abstract, §I)] The paper repeatedly distinguishes 'topologically trivial' and 'topologically non-trivial' regimes but never defines the topological invariant used. The central claim that a real spectrum does not imply a trivial NHMBL phase requires simultaneous measurement of a topological quantity (e.g., winding number, spectral flow under twisted boundary conditions, or an equivalent many-body invariant) and the spectral reality. Without this definition, the claim is not falsifiable. The topology diagnostic and its relation to TRS must be stated explicitly.
[Skin effect claim (Abstract)] The claim that the entire topologically non-trivial ergodic regime under PBC does not always give rise to OBC skin modes is not supported by any boundary-condition comparison. To establish this, the authors need to show OBC eigenstate density or participation ratio as a function of parameters and system size, and ideally identify the threshold in the hopping exponent where the skin effect disappears. No such analysis is present in the submitted text.

minor comments (4)

[Abstract] Typo: 'Our findings thus advances' should be 'Our findings thus advance'. Also 'quaisperiodic' in §I should be 'quasiperiodic'.
[§I / References] The introduction references several models and results (e.g., Refs. [37,41,44,65,67]) without defining the corresponding Hamiltonians; adding a brief model orientation in the introduction would help the reader.
[Manuscript completeness] The text ends after the introduction and references; no conclusions or summaries of numerical findings are present. The manuscript appears truncated or incomplete in its current form.
[References / Methods] The reference list mentions software and diagnostics such as QuSpin [80] and complex spacing ratios [81], but the methods are never described. If these tools are used, the relevant definitions and statistical procedures must appear in the main text.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity identifiable from the available text; the reported phases are presented as numerical findings, not as renamings of fitted inputs.

full rationale

The provided portion of the manuscript (abstract, introduction, and references) contains no derivation of the central claims from fitted parameters or from self-citing uniqueness theorems. The claims—existence of a topologically trivial intermediate regime with multifractal states and real spectrum, destruction of mobility edges by interactions, and suppression of skin modes under long-range hopping—are stated as results of exact diagonalization and finite-size analysis. The only self-citations (Refs. [40] and [79]) appear in lists of background literature on non-Hermitian MBL and skin effects; they are not used as load-bearing justifications for the new phase diagram. No equation-level reduction, fitted-input-renamed-as-prediction, or self-definitional identification can be exhibited from the available text. The concern that finite-size scaling may misidentify the intermediate regime is a correctness/finite-size risk, not circularity. Therefore the honest finding is no significant circularity.

Assumptions & free parameters 0 free parameters · 3 assumptions · 0 invented entities

The available excerpt does not specify the model parameters or any fitting procedure. The physical parameters (asymmetric hopping strength, power-law exponent, interaction strength, quasiperiodic potential amplitude) are likely scanned, not fitted. No new entities are postulated.

assumptions (3)

domain assumption The non-Hermitian Hamiltonian with asymmetric hopping and quasiperiodic potential can be treated as a physical open quantum system, and its spectrum and eigenstates capture the phases.
The abstract interprets real spectra as restoring time-reversal symmetry, which presumes standard non-Hermitian many-body physics.
domain assumption Finite-size exact diagonalization results extrapolate to the thermodynamic limit for the reported phase boundaries.
The claims about intermediate and NHMBL phases depend on scaling from small chains, which is the standard assumption in this literature.
domain assumption The definition of multifractality via participation entropy or similar scaling measures is a reliable phase diagnostic.
Abstract says states are 'primarily multifractal in nature', which relies on established multifractal analysis.

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Cite this review

Pith. "Pith review of Emergence of non-trivial phases in interacting non-Hermitian quasiperiodic chains with power-law hopping." pith.science (2026). https://pith.science/paper/KNDBUGUS

@misc{pith2026250814724,
  author       = {Pith},
  title        = {Pith review of: Emergence of non-trivial phases in interacting non-Hermitian quasiperiodic chains with power-law hopping},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KNDBUGUS}},
  note         = {Machine review of arXiv:2508.14724}
}

read the original abstract

In the last few years, several works have identified the concurrence of the spectral, delocalization-localization and topological phase transitions in non-Hermitian quasiperiodic systems in the presence of time-reversal symmetry (TRS), with or without interaction. In this work, we investigate one-dimensional interacting non-Hermitian quasiperiodic lattices with asymmetric power-law hopping and unveil that although the Hamiltonian respects the TRS, the reality of the eigenspectrum does not necessarily indicate a topologically trivial non-Hermitian many-body localization (NHMBL) regime. In fact, we reveal the emergence of a topologically trivial intermediate regime, where the states that are primarily multifractal in nature can also possess a fully real spectrum, thereby restoring the TRS before crossing over to the NHMBL phase. Moreover, in the entire intermediate regime, the interaction completely destroys the multifractal and mobility edges observed in the non-interacting counterpart. Besides, we unveil that due to the long-range nature of the hopping, the entire topologically non-trivial ergodic regime under the periodic boundary condition does not always give rise to boundary localized skin modes under the open boundary condition. Our findings thus advances and deepens the understanding about the emergence of non-trivial phases due to the interplay of interaction and long-range hopping in non-Hermitian quasiperiodic systems.

Discussion (0). Continue with ORCID to comment.

Reference graph

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