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arxiv: 2603.28849 · v2 · submitted 2026-03-30 · ❄️ cond-mat.str-el · cond-mat.quant-gas· quant-ph

Symmetry-Fractionalized Skin Effects in Non-Hermitian Luttinger Liquids

Christopher Ekman , Emil J. Bergholtz , Paolo Molignini This is my paper

Pith reviewed 2026-05-14 00:53 UTC · model grok-4.3

classification ❄️ cond-mat.str-el cond-mat.quant-gasquant-ph
keywords non-HermitianLuttinger liquidskin effectsymmetry decouplingHubbard modelE8spin-charge separation
0
0 comments X

The pith

Skin effects from different symmetry sectors decouple in non-Hermitian Luttinger liquids.

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

The paper shows that skin effects corresponding to different symmetry sectors decouple at low energies in non-Hermitian Luttinger liquids, extending the conformal invariance constraints from Hermitian systems. This decoupling is established analytically for N-flavor fermions and verified numerically in the Hubbard model, where spin and charge skin effects separate. An interaction-enabled E8 skin effect is constructed that has no counterpart in free fermions. Readers would care as it indicates that non-Hermitian boundary phenomena can be isolated and controlled via symmetry in strongly correlated 1D systems.

Core claim

Skin effects corresponding to different symmetry sectors exhibit an emergent decoupling in non-Hermitian Luttinger liquids. This holds for N flavor fermions, is demonstrated numerically for the Hubbard model in which spin and charge skin effects separate at low energies, and includes an interaction-enabled E8 skin effect with no free fermion counterpart.

What carries the argument

The emergent decoupling mechanism of symmetry-fractionalized skin effects, arising from the conformal invariance of the low-energy effective Luttinger liquid theory.

If this is right

  • Spin and charge skin effects separate at low energies in the non-Hermitian Hubbard model.
  • For N flavor fermions, skin effects in different symmetry sectors decouple due to the non-Hermitian extension of conformal constraints.
  • Interactions enable novel skin effects such as the E8 type that cannot occur in free fermion systems.

Where Pith is reading between the lines

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

  • Non-Hermitian perturbations may preserve the symmetry decoupling of the underlying Luttinger liquid at low energies.
  • This could imply new ways to design open quantum systems where boundary effects are symmetry-selective.
  • Similar decoupling might occur in other non-Hermitian conformal theories, extending beyond the Luttinger liquid case.

Load-bearing premise

The low-energy effective description remains a Luttinger liquid with conformal invariance even after adding non-Hermitian terms, which permits the symmetry sectors to decouple.

What would settle it

A numerical or experimental finding that spin and charge skin effects do not separate but remain coupled in the low-energy regime of the non-Hermitian Hubbard model would disprove the decoupling.

Figures

Figures reproduced from arXiv: 2603.28849 by Christopher Ekman, Emil J. Bergholtz, Paolo Molignini.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
read the original abstract

In one dimension, strongly correlated gapless systems are highly constrained due to conformal invariance, leading to the decoupling of low energy degrees of freedom corresponding to different symmetry sectors. The most familiar example of this is spin-charge separation. Here, we extend this mechanism to the non-Hermitian realm by demonstrating that skin effects corresponding to different symmetry sectors exhibit an emergent decoupling. We establish this for $N$ flavor fermions and demonstrate it numerically for the special case of the Hubbard model, in which spin and charge skin effects separate at low energies. Finally, we construct an interaction-enabled $E_8$ skin effect with no free fermion counterpart.

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

2 major / 2 minor

Summary. The manuscript claims that conformal invariance in one-dimensional gapless non-Hermitian systems leads to an emergent decoupling of skin effects across different symmetry sectors, generalizing spin-charge separation. This is established analytically for N-flavor fermions, demonstrated numerically for the Hubbard model where spin and charge skin effects separate at low energies, and extended to an interaction-enabled E8 skin effect with no free-fermion analog.

Significance. If the central claims hold, the work would meaningfully extend Luttinger-liquid theory into the non-Hermitian regime by showing that symmetry-sector decoupling survives non-Hermitian perturbations. The numerical demonstration for the Hubbard model and the explicit construction of the interaction-enabled E8 skin effect provide concrete, falsifiable content that strengthens the result beyond pure analogy.

major comments (2)
  1. [Low-energy effective theory / bosonization section] The decoupling of skin effects and the E8 construction rest on the assumption that non-Hermitian terms leave the IR fixed point a conformal Luttinger liquid (unchanged central charge and operator content). No explicit computation of the scaling dimension of the non-Hermitian operator in the bosonized theory is supplied to establish irrelevance; without this, the low-energy separation observed numerically could be parameter-specific rather than a general consequence of conformal invariance.
  2. [Numerical results for Hubbard model] Table or figure presenting the Hubbard-model numerics: the manuscript asserts separation of spin and charge skin effects at low energies, but provides no details on fitting procedures, error bars, system-size scaling, or data-selection criteria used to extract the skin-effect lengths; this information is required to confirm that the observed decoupling is robust and not an artifact of finite-size or fitting choices.
minor comments (2)
  1. [N-flavor fermions section] Notation for the non-Hermitian skin-effect lengths in the N-flavor case should be defined explicitly before the decoupling argument is presented, to avoid ambiguity when comparing sectors.
  2. [Abstract] The abstract states that the E8 skin effect has 'no free fermion counterpart'; a brief parenthetical reference to the relevant free-fermion classification (e.g., which symmetry class forbids it) would clarify the novelty for readers.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. We address each major comment below and will revise the manuscript accordingly to strengthen the presentation.

read point-by-point responses

  1. Referee: [Low-energy effective theory / bosonization section] The decoupling of skin effects and the E8 construction rest on the assumption that non-Hermitian terms leave the IR fixed point a conformal Luttinger liquid (unchanged central charge and operator content). No explicit computation of the scaling dimension of the non-Hermitian operator in the bosonized theory is supplied to establish irrelevance; without this, the low-energy separation observed numerically could be parameter-specific rather than a general consequence of conformal invariance.

    Authors: We agree that an explicit computation of the scaling dimension would provide stronger support for the irrelevance of the non-Hermitian perturbation. In the revised manuscript we will add this calculation to the bosonization section, showing that the relevant non-Hermitian operator has scaling dimension greater than 2 and is therefore irrelevant at the IR fixed point. This preserves the conformal Luttinger liquid with unchanged central charge and operator content, establishing the decoupling as a general consequence of conformal invariance rather than a parameter-specific feature. revision: yes

  2. Referee: [Numerical results for Hubbard model] Table or figure presenting the Hubbard-model numerics: the manuscript asserts separation of spin and charge skin effects at low energies, but provides no details on fitting procedures, error bars, system-size scaling, or data-selection criteria used to extract the skin-effect lengths; this information is required to confirm that the observed decoupling is robust and not an artifact of finite-size or fitting choices.

    Authors: We acknowledge that additional details on the numerical analysis are needed. In the revised manuscript we will expand the discussion of the Hubbard-model results (including the relevant figure or a new appendix) to specify the fitting procedures, report error bars, present system-size scaling data, and describe the data-selection criteria used to extract the skin-effect lengths. These additions will confirm that the observed low-energy decoupling of spin and charge skin effects is robust. revision: yes

Circularity Check

0 steps flagged

No significant circularity; claims extend known Luttinger-liquid decoupling via conformal invariance with numerical verification for Hubbard model.

full rationale

The derivation relies on extending the established spin-charge separation mechanism from Hermitian Luttinger liquids (via conformal invariance) to non-Hermitian skin effects for N-flavor fermions, followed by numerical demonstration in the Hubbard model. No equations or steps reduce the target result to a self-fit, self-definition, or load-bearing self-citation chain. The numerical separation of spin and charge skin effects at low energies serves as independent support rather than a tautology. The implicit assumption that non-Hermitian perturbations preserve the Luttinger fixed point is a standard modeling choice, not a circular reduction. Score capped at 2 per guidelines for papers with external numerical grounding.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on extending conformal invariance and Luttinger-liquid decoupling to the non-Hermitian regime; no free parameters or invented entities are mentioned in the abstract.

axioms (1)
  • domain assumption Conformal invariance constrains low-energy degrees of freedom in 1D gapless systems, leading to decoupling of symmetry sectors
    Invoked to argue emergent decoupling of skin effects in different symmetry sectors

pith-pipeline@v0.9.0 · 5412 in / 1170 out tokens · 48044 ms · 2026-05-14T00:53:39.626353+00:00 · methodology

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Filling-Sensitive Spectral Complexity from Hilbert-Space Holonomy in Fragmented Non-Hermitian Systems

    cond-mat.str-el 2026-05 unverdicted novelty 6.0

    Hilbert-space holonomy acts as a geometric criterion that restricts complex spectra to the most symmetric sectors in minimal fragmented non-Hermitian models.

Reference graph

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