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Point-gap topology in amorphous non-Hermitian quantum systems

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Pith's one-line read In amorphous non-Hermitian chains, the real-space winding number computed from the singular-value decomposition stays quantized and predicts edge states even when the eigenvalue spectrum is unstable.

desk verdict A useful SVD-based probe for amorphous non-Hermitian chains, but the central correspondence between vanishing singular values and eigenstates is unproven and contradicted by the paper's own pseudospectra. read the letter →

arxiv 2608.08687 v3 pith:ZRBCR4CD submitted 2026-08-09 quant-ph

Xue-Min Yang , Mu Zhou , Deng-Feng Li , Jian Li , Jia-Ji Zhu , Li Li , Qiu-Chi Chen , Xin-Qi Xu
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Hao-Peng Zhang Hong Wu
This is my paper · ORCID
classification quant-ph
keywords non-Hermitiantopologypoint-gapamorphoussystemssingularvaluedecompositionskineffectreal-spacewindingnumberspectralinstabilitypseudospectrum
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

This paper argues that in one-dimensional amorphous non-Hermitian systems the ordinary eigenvalue spectrum is too unstable to reveal point-gap topology, so topological edge states must be diagnosed through singular values instead. It establishes that stable zero-mode singular states of $H-E_b I$ correspond to mid-gap eigenstates of $H$ in the thermodynamic limit, and it constructs a real-space winding number $V(E_b)$ from the singular-value decomposition that stays sharply quantized even under strong disorder. If the correspondence holds, singular-value spectra become a reliable experimental probe of non-Hermitian topology in systems, such as amorphous lattices, where translation symmetry is absent.

What carries the argument

The engine of the argument is the singular-value decomposition $H-E_b I=U_A S U_B^\dagger$ and the enlarged Hermitian Hamiltonian $\tilde H(E_b)$ with chiral symmetry $\Sigma\tilde H(E_b)\Sigma^{-1}=-\tilde H(E_b)$. From $U_A$ and $U_B$ and a position matrix $P$ encoding real-space phases, the paper defines the winding number $V(E_b)=\frac{1}{2\pi i}\operatorname{Tr}\ln(P_A P_B^\dagger)$, whose modulus counts the zero-mode edge states of $\tilde H(E_b)$ and hence the edge states of $H$ at energy $E_b$. The singular values $s_n$ are square roots of eigenvalues of the positive Hermitian operator $(H-E_b I)^\dagger(H-E_b I)$, which gives the singular spectrum the stability that the non-Hermitian eigenvalue spectrum lacks.

What would settle it

Take a disorder realization of the amorphous chain and a reference energy $E_b$ where $s_{\min}(H-E_b I)$ is numerically zero; compute the distance $\min_n|\lambda_n-E_b|$ from the eigenvalues to $E_b$ as the system size $L$ grows. If that distance stays of order one while $s_{\min}$ keeps vanishing, the zero-mode singular vector is not converging to an eigenstate and the correspondence is falsified.

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Extended reading notes

Core claim

The central claim is that for the amorphous non-Hermitian chain with random site positions and exponential hopping, the real-space winding number $V(E_b)=\frac{1}{2\pi i}\operatorname{Tr}\ln(P_A P_B^\dagger)$ computed solely from the SVD of $H-E_b I$ is sharply quantized and counts the number of topologically protected edge states at energy $E_b$ in the thermodynamic limit. This remains true even though the eigenvalue spectrum is severely unstable: as the system size grows, the complex-plane eigenvalue distribution becomes structureless and the pseudospectrum balloons outward, while the singular values of $H-E_b I$ remain robust because they are eigenvalues of the Hermitian operator $(H-E_b I)^\dagger(H-E_b I)$. The paper therefore proposes that the number of zero-mode singular states of $H-E_b I$ is linked to the number of stable $E_b$-mode states of $H$, and that the non-Hermitian skin effect should be identified through these singular vectors rather than through eigenstate localization.

Load-bearing premise

The argument hinges on assuming that a vanishing smallest singular value of $H-E_b I$ forces a true eigenstate of $H$ at $E_b$ in the thermodynamic limit, even though non-Hermitian matrices can have tiny singular values far from any eigenvalue.

Editorial extensions

If this is right

  • Even when the eigenvalue spectrum shows no clear gap, the SVD-based winding number $V(E_b)$ identifies the topological phase and predicts edge states in finite amorphous samples.
  • The number of zero-mode singular values of $H-E_b I$ equals the number of stable mid-gap eigenstates in the thermodynamic limit, making singular values a practical diagnostic for non-Hermitian topology.
  • The real-space invariant extends point-gap bulk-boundary correspondence to disordered systems without translational symmetry, including amorphous lattices.
  • On experimental platforms such as waveguide arrays or cold atoms in optical tweezers, the topological edge states can be detected by preparing a zero-mode singular state and measuring a generalized Loschmidt echo that stays near unity.

Reading between the lines

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

  • If the correspondence is generic, singular-value invariants could replace spectral winding numbers for disordered non-Hermitian systems in higher dimensions and with multiple bands, since the same Hermitian-stability argument applies.
  • The proposed redefinition of the skin effect implies that skin modes should be diagnosed by zero-mode singular vectors rather than by eigenstate localization; this would change how experiments identify skin modes in systems with strong disorder.
  • A direct numerical test on small random matrices would be to fix $E_b$, add a weak perturbation to the hopping amplitudes, and compare how much the smallest singular values move versus how much the eigenvalues move; the paper's claim predicts the singular values remain nearly fixed.
  • The framework connects to pseudospectrum theory: it suggests that the low singular values inside the $\varepsilon$-pseudospectrum carry topological integer data even where the spectrum itself is unstable.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 6 minor

Summary. This manuscript studies point-gap topology in a one-dimensional amorphous non-Hermitian chain with random site positions, exponential hopping, and nonreciprocal hopping strength γ. Starting from the observation that the eigenvalue spectrum of the disordered non-Hermitian Hamiltonian is highly unstable, with large ε-pseudospectra extending far beyond the eigenvalues (Fig. 3), the authors propose that stable zero-mode singular states of H−E_b I are in one-to-one correspondence with mid-gap eigenstates of H in the thermodynamic limit (Eqs. (8)–(9)). They construct an enlarged Hermitian operator H̃(E_b) with chiral symmetry and a real-space winding number V(E_b) = (1/2πi) Tr ln(P_A P_B†) built from the SVD of H−E_b I, and claim that |V(E_b)| predicts the number of topologically protected edge states of H at energy E_b. The numerics show sharply quantized V(0) for several system sizes (Fig. 4), a (t, γ) topological phase diagram (Fig. 5), and coincidence of the nontrivial V(E_b) region with the small-s_min(H−E_b I) region (Fig. 6). An experimental detection protocol based on the Loschmidt echo is sketched.

Significance. The proposed strategy is potentially valuable: singular values of H−E_b I are Lipschitz-stable under bounded perturbations, a Hermitian-stability property the paper correctly emphasizes, so they offer a route to probing point-gap topology in systems where the eigenvalue spectrum is unusably unstable. Extending the SVD-based approach of Refs. [85–87] from translationally invariant and Floquet systems to amorphous systems without any periodicity is a natural and worthwhile generalization, and the paper states its model and diagnostics clearly. The finitary numerical claims — near-integer V(0), edge-localized lowest singular vectors, and a clean phase boundary — are plausible and constitute a falsifiable prediction if supported by error statistics. However, the manuscript's central interpretive step, the thermodynamic-limit correspondence between zero singular values and true eigenstates, is asserted without proof and is false for general non-normal operators; the paper's own pseudospectra demonstrate the danger. The contribution is therefore conditional on repairing that step.

major comments (3)
  1. [Eqs. (8)–(9) and Fig. 3] The thermodynamic-limit correspondence asserted in the paragraph containing Eqs. (8)–(9) is the load-bearing step of the paper, and the implication that lim_{L→∞} s_min(H−E_b I)=0 implies a normalizable eigenstate v_n of H with eigenvalue E_b is not valid for non-normal operators. The standard counterexample is the unilateral shift: for the finite truncations S_N, s_min(zI−S_N) decays to zero for every |z|<1, yet the infinite shift has no eigenvalue in the open unit disk, and the limiting singular vectors converge to eigenvectors of S*, not of S. This is not a remote pathology here, because the paper's own Figs. 3(e)–(h) show large regions where s_min(zI−H)<10^{-2} far from any eigenvalue; by the proposed implication those regions would be filled with eigenstates, contradicting Figs. 3(a)–(d). Consequently, the reading of Fig. 6(b) as evidence that the small-s_min region hosts protected eigenstates of H at energy E_b is unproven; those modes could equally be pseudomodes of the residual or continuous spectrum. I ask the authors to either (i) supply a convergence argument (for example via strong resolvent convergence plus a spectral-projection or Fredholm-index argument) showing that the edge-localized zero-mode singular vectors counted by V(E_b) lie in the point spectrum of the infinite-volume H−E_b I, or (ii) provide a direct numerical verification for this model: for the E_b values with V(E_b)≠0, compute the distance from E_b to the spectrum of H and the overlap of the singular vector with the corresponding eigenvector as functions of L. The scaling of s_min with L (algebraic versus exponential) should be reported, since exponential decay is the signature of pseudomodes rather than of an approaching eigenvalue.
  2. [Eqs. (10)–(12), Figs. 4 and 6] The invariant V(E_b) in Eq. (11) is constructed from the SVD of the open-chain matrix H−E_b I over all sites, with the phase matrix P of Eq. (12) covering the full chain and the trace running over all singular vectors including the edge-localized ones; the lowest singular vectors of this same SVD are then identified as the predicted edge states. The text's claim that V(E_b) is computed solely from the bulk SVD data and predicts the edge-state count is therefore, as implemented, a self-consistency statement within a single decomposition rather than an independent bulk-boundary correspondence, in contrast to W(E_b) in Eq. (5), which at least uses the windowed trace Tr'. To support the predictive claim, the authors should compute V(E_b) from a bulk-windowed trace or from an auxiliary construction that does not use the edge data (for example, a periodically reordered arrangement of the same disorder realization), and show that this independent quantity still matches the number of edge-localized zero singular modes.
  3. [Figs. 4 and 5 (statistics)] The central empirical claims — that V(0) is sharply quantized and that the phase boundary in Fig. 5 is sharply resolved — are presented without statistical support: Figs. 2, 4, and 6 give disorder averages over 50–1000 realizations but no standard deviations, quantiles, or per-realization distributions, and Fig. 5 shows a single averaged color map with 100 realizations per grid point. Because V(E_b) is a phase-winding type quantity, its per-realization distribution is essential: the authors should state the quantization criterion (for example, the fraction of realizations with |V−1|<ε for a stated ε) and report the typical fluctuation scale. Without this, the reader cannot distinguish genuine quantization from an artifact of averaging.
minor comments (6)
  1. [Eq. (5) vs Eq. (11)] The claimed advantage of V(E_b) over W(E_b) in terms of higher accuracy and less fluctuation is not demonstrated; no plot comparing the two quantities on the same disorder realizations is provided.
  2. [Eqs. (3)–(4)] The diagnostics mcom and WIPR weight by the site index j and |j−L/2|, although the physical positions x_j are randomly distributed over [0, 2L]; for large density fluctuations the index is not a faithful spatial coordinate, and the actual positions x_j should be used instead.
  3. [Eq. (11)] The branch-cut convention used to evaluate Tr ln in Eq. (11) is not specified; a brief statement of how V(E_b) is evaluated as an integer in finite systems would help the reader reproduce the calculation.
  4. [Entire manuscript] The manuscript contains numerous rendering problems (for example, '2Lsites', 'H−E bI', 'values min' in the Fig. 6 caption, and missing spaces in the author list), which should be corrected.
  5. [Near Fig. 6 and Conclusion] The announced redefinition of the non-Hermitian skin effect is not stated as a precise criterion; the authors should give an operational definition (for example, scaling of boundary weight with system size) that distinguishes skin states from ordinary edge-localized states.
  6. [Paragraph after Eq. (12)] The counting of |2V(E_b)| zero-mode edge states of H̃ implicitly assumes dim ker(H−E_b I) = dim ker(H†−E_b^* I) = |V(E_b)|; in general H̃ has dim ker(A)+dim ker(A†) zero modes, which need not equal 2|V(E_b)|, so the statement should be qualified.

Circularity Check

2 steps flagged · score 6.0 of 10

Central 'zero-mode singular state ↔ eigenstate' correspondence is the definition of zero singular value, and the V(E_b) verification compares two functionals of the same SVD.

  1. self definitional [Section 'The robust point-gap topology in real space', Eqs. (8)-(9)]
    "When lim_{L→∞} s_min(H−E_b I) = 0, the [(H−E_b I)v_n]_{L→∞} = 0 implies the system supports a state with wave function v_n and eigenvalue E_b."

    For finite matrices, s_n=0 is equivalent to (H−E_b I)v_n=0: a zero singular value is by definition the same condition as having an eigenvector of H with eigenvalue E_b. The paper presents this linear-algebra identity as the newly introduced 'correspondence' that carries the later identification of singular edge states with protected eigenstates. The thermodynamic-limit step is an additional unproved assumption about convergence of v_n and of the operator sequence, and it is false for generic non-normal pseudospectral families, as the paper's own Fig. 3 illustrates. Thus the central premise is the definitional equivalence between zero singular values and kernel vectors, plus a limit interchange that is not established.

  2. self definitional [Section 'The robust point-gap topology in real space', Fig. 6 and surrounding text]
    "Panel (b) confirms that the region of zero-mode singular values coincides with the topologically nontrivial region identified in panel (a), demonstrating that zero-mode singular values faithfully signal the existence of topological edge states."

    The invariant V(E_b) in Eq. (11) is built from P_A=U_A† P U_A and P_B=U_B† P U_B, where U_A and U_B come from the same SVD H−E_b I=U_A S U_B† that also supplies the zero-mode singular vectors later called edge states. Consequently, the 'coincidence' between V≠0 and zero singular values is a comparison of two functionals of one and the same SVD, not a prediction checked against an independent eigenstate calculation. The paper explicitly says the eigenvalue edge state is invisible in the spectrum, so the verification loop closes entirely within the SVD; the predicted protected states are never exhibited as eigenstates of H in an independent calculation.

full rationale

The paper's derivation contains no fitted parameters and no self-citation chain that forces the central result: the SVD-based invariant is defined in the text, and the robustness of singular values is supported by standard Hermitian-stability arguments plus references. However, the load-bearing 'correspondence' between stable zero-mode singular states and mid-gap eigenstates is, at exact zero, the definition of a singular value (s_n=0 iff (H−E_b I)v_n=0), and the thermodynamic-limit generalization is assumed rather than proved. The numerical demonstration is also self-referential in an important way: V(E_b) and the zero-mode edge states are both extracted from the SVD of the same finite open-boundary H−E_b I, with no independent eigenstate benchmark, so the apparent agreement in Fig. 6 is in part by construction. Self-citations [86,87] are present but are applications of the same SVD diagnostic by overlapping authors; they are not the unique load-bearing support, because the basic zero-singular-value/eigenvector identity is standard linear algebra and Ref. [85] is external. The paper does have independent content in the demonstrated stability and sharp quantization of V, which is why the circularity is partial rather than total; the score reflects one central prediction reducing by construction to the definition of zero singular values and to the same SVD data used to define the invariant.

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

No free parameters are fitted to data: t, γ and d_min are model controls scanned in the phase diagram, and disorder averages are done over explicitly stated numbers of realizations. Three load-bearing premises are imported or asserted: the thermodynamic-limit correspondence between zero singular values and eigenstates, the chiral winding bulk-boundary theorem for the enlarged Hamiltonian, and the claim that V(E_b) computed from the open chain is a bulk quantity. The first is the most fragile because the paper's own pseudospectrum analysis shows small singular values far from eigenvalues.

assumptions (3)
  • ad hoc to paper Thermodynamic-limit correspondence: a sequence of unit vectors annihilated by H−E_b I in the L→∞ limit gives a genuine normalizable eigenstate of H with eigenvalue E_b.
    Load-bearing for the central correspondence; asserted near Eqs. (8)-(9) without proof and not generally true for non-normal operators.
  • domain assumption The real-space winding number V(E_b) of the enlarged chiral Hamiltonian counts zero-mode edge states (chiral bulk-boundary correspondence).
    Adopted from Refs. [85,118,119] in the paragraph after Eq. (11); no derivation is given in this paper.
  • domain assumption The open-chain SVD data used to compute V(E_b) represents bulk topology; boundary states do not affect the trace logarithm.
    Eq. (11) uses all 2L sites without the boundary exclusion applied to W(E_b) in Eq. (5); the paper assumes O(1) edge states cannot change the O(L) invariant.

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Pith. "Pith review of Point-gap topology in amorphous non-Hermitian quantum systems." pith.science (2026). https://pith.science/paper/ZRBCR4CD

@misc{pith2026260808687,
  author       = {Pith},
  title        = {Pith review of: Point-gap topology in amorphous non-Hermitian quantum systems},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ZRBCR4CD}},
  note         = {Machine review of arXiv:2608.08687}
}
read the original abstract

Recent studies have revealed that not only does the correspondence between spectral winding numbers and skin modes break down in non-Hermitian systems, but the energy spectrum itself is highly sensitive to generic perturbations, system size, and boundary conditions. In amorphous non-Hermitian systems, where the positions of lattice sites are uncertain, the spectral instability becomes even more severe, making it difficult to identify stable topological edge states from the eigenvalue spectrum alone. To overcome this challenge, we introduce a correspondence between stable zero-mode singular states and mid-gap states of the energy spectrum in the thermodynamic limit. Because the singular value spectrum is highly robust against small perturbations and variation in size, topological edge states can be reliably probed via singular values even in finite-sized systems. Based on the singular-value decomposition of the Hamiltonian, we construct a topological invariant in real space to characterize the associated topologically protected edge states. Our approach provides a general strategy for exploring point-gap topology in real space and redefine the non-Hermitian skin effect from a new perspective.

Figures

Figures reproduced from arXiv: 2608.08687 by the authors.

Figure 1
Figure 1. FIG. 1. Schematics of the amorphous model on a chain. [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Characterization of the non-Hermitian skin effect via IPR, WIPR, mcom, and the real-space winding number for the [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Eigenvalue spectra and pseudospectra of the 1D non-Hermitian amorphous chain defined by Eq. ( [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (2 more)
Figure 5
Figure 5. Figure 5: FIG. 5. Topological phase diagram of the 1D non-Hermitian [PITH_FULL_IMAGE:figures/full_fig_p005_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. (a) Real-space topological invariant [PITH_FULL_IMAGE:figures/full_fig_p005_6.png]

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Works this paper leans on

123 extracted references · 63 canonical work pages

  1. [1]

    J. C. Budich and E. J. Bergholtz, Non-Hermitian topo- logical sensors, Phys. Rev. Lett.125, 180403 (2020)

    2020

  2. [2]

    Koch and J

    F. Koch and J. C. Budich, Quantum non-Hermitian topological sensors, Phys. Rev. Res.4, 013113 (2022)

    2022

  3. [3]

    M. A. Bandres, S. Wittek, G. Harari, M. Parto, J. Ren, M. Segev, D. N. Christodoulides, and M. Khajavikhan, Topological insulator laser: Experiments, Science359, 6381 (2018)

    2018

  4. [4]

    K. Sone, Y. Ashida, and T. Sagawa, Exceptional mode topological surface laser, Phys. Rev. B105, 235426 (2022)

    2022

  5. [5]

    Ezawa, N

    M. Ezawa, N. Ishida, Y. Ota, and S. Iwamoto, Su- persymmetric non-Hermitian topological interface laser, Phys. Rev. B107, 085302 (2023)

    2023

  6. [6]

    J. Rao, J. Ding, Q. Guo, J. He, and X. Ni, Unidirectional-like edge transport induced by non- Hermitian skin effects (2026), arXiv:2606.10291 [physics.optics]

    work page Pith review arXiv 2026

  7. [7]

    C. C. Wanjura, M. Brunelli, and A. Nunnenkamp, Topological framework for directional amplification in driven-dissipative cavity arrays, Nat. Commun.11, 3149 (2020)

    2020

  8. [8]

    Esaki, M

    K. Esaki, M. Sato, K. Hasebe, and M. Kohmoto, Edge states and topological phases in non-Hermitian systems, Phys. Rev. B84, 205128 (2011)

    2011

Show all 123 references
  1. [9]

    T. E. Lee, Anomalous edge state in a non-Hermitian lattice, Phys. Rev. Lett.116, 133903 (2016)

    2016

  2. [10]

    Xu, S.-T

    Y. Xu, S.-T. Wang, and L.-M. Duan, Weyl exceptional rings in a three-dimensional dissipative cold atomic gas, Phys. Rev. Lett.118, 045701 (2017)

    2017

  3. [11]

    Yao and Z

    S. Yao and Z. Wang, Edge states and topological invari- ants of non-Hermitian systems, Phys. Rev. Lett.121, 086803 (2018)

    2018

  4. [12]

    H. Shen, B. Zhen, and L. Fu, Topological band theory for non-Hermitian Hamiltonians, Phys. Rev. Lett.120, 146402 (2018)

    2018

  5. [13]

    Zhou and J

    L. Zhou and J. Gong, Non-Hermitian Floquet topolog- ical phases with arbitrarily many real-quasienergy edge states, Phys. Rev. B98, 205417 (2018)

    2018

  6. [14]

    Yokomizo and S

    K. Yokomizo and S. Murakami, Non-Bloch band theory of non-Hermitian systems, Phys. Rev. Lett.123, 066404 (2019)

    2019

  7. [15]

    Kawabata, K

    K. Kawabata, K. Shiozaki, M. Ueda, and M. Sato, Sym- metry and topology in non-Hermitian physics, Phys. Rev. X9, 041015 (2019)

    2019

  8. [16]

    J. Y. Lee, J. Ahn, H. Zhou, and A. Vishwanath, Topo- logical correspondence between Hermitian and non- Hermitian systems: Anomalous dynamics, Phys. Rev. Lett.123, 206404 (2019)

    2019

  9. [17]

    Wu, B.-Q

    H. Wu, B.-Q. Wang, and J.-H. An, Floquet second-order topological insulators in non-Hermitian systems, Phys. Rev. B103, L041115 (2021)

    2021

  10. [18]

    Y. Li, C. Fan, X. Hu, Y. Ao, C. Lu, C. T. Chan, D. M. Kennes, and Q. Gong, Effective Hamiltonian for pho- tonic topological insulator with non-Hermitian domain walls, Phys. Rev. Lett.129, 053903 (2022)

    2022

  11. [19]

    C.-X. Guo, S. Chen, K. Ding, and H. Hu, Exceptional non-Abelian topology in multiband non-Hermitian sys- tems, Phys. Rev. Lett.130, 157201 (2023)

    2023

  12. [20]

    Jezequel and P

    L. Jezequel and P. Delplace, Non-Hermitian spectral flows and Berry-Chern monopoles, Phys. Rev. Lett. 130, 066601 (2023)

    2023

  13. [21]

    Bai, J.-Z

    K. Bai, J.-Z. Li, T.-R. Liu, L. Fang, D. Wan, and M. Xiao, Nonlinear exceptional points with a complete basis in dynamics, Phys. Rev. Lett.130, 266901 (2023)

    2023

  14. [22]

    Okuma and M

    N. Okuma and M. Sato, Non-Hermitian topological phe- nomena: A review, Annu. Rev. Condens. Matter Phys. 14, 83 (2023)

    2023

  15. [23]

    Jangjan, L

    M. Jangjan, L. Li, L. E. F. Foa Torres, and M. V. Hosseini, Topological phases of commensurate or incom- mensurate non-Hermitian Su-Schrieffer-Heeger lattices, Phys. Rev. B109, 205142 (2024)

    2024

  16. [24]

    Li, J.-W

    M.-W. Li, J.-W. Liu, X. Wang, W.-J. Chen, G. Ma, and J.-W. Dong, Topological temporal boundary states in a non-Hermitian spatial crystal, Phys. Rev. Lett.135, 187101 (2025)

    2025

  17. [25]

    K.-X. Hu, C. Luo, J. Zhang, S. Liu, W.-X. Cui, J. Cao, S. Zhang, and H.-F. Wang, Bulk-boundary correspon- dence in non-Hermitian class-d † topological systems, Phys. Rev. A112, 052209 (2025)

    2025

  18. [26]

    Zhang, Y

    M. Zhang, Y. Zhang, S. Li, Y.-A. Li, Y. Wei, R. Tian, T. Wu, H. Shi, H. Gao, F. Li, and B. Liu, Observa- tion of non-Hermitian bulk-boundary correspondence in nonchiral nonunitary quantum dynamics of single pho- tons, Phys. Rev. Lett.135, 213601 (2025)

    2025

  19. [27]

    E. Ma, K. Zhang, and Z. Song, Dynamically stable topo- logical edge states in an extended Su-Schrieffer-Heeger ladder with balanced perturbation, Phys. Rev. B112, 195134 (2025)

    2025

  20. [28]

    Wu and L

    H. Wu and L. Jin, Topological zero modes from the in- terplay ofPTsymmetry and anti-PTsymmetry, Phys. Rev. B112, 125146 (2025)

    2025

  21. [29]

    Yuce and H

    C. Yuce and H. Ramezani, Topological states in a non- Hermitian two-dimensional Su-Schrieffer-Heeger model, Phys. Rev. A100, 032102 (2019)

    2019

  22. [30]

    S. A. A. Ghorashi and M. Sato, Topological reality switch: Towards bulk-boundary selective lasing (2025), arXiv:2507.02038 [quant-ph]

    2025 arXiv

  23. [31]

    Zhang, J

    G. Zhang, J. Kang, C. Wu, D. Zheng, Y. Zhou, W. Bao, and G. Chen, Multigap topology engineering in non- 7 Hermitian superlattices, Phys. Rev. A112, 043549 (2025)

    2025

  24. [32]

    Zhou, Topology and edge modes surviving criticality in non-hermitian Floquet systems, Phys

    L. Zhou, Topology and edge modes surviving criticality in non-hermitian Floquet systems, Phys. Rev. Res.8, L022026 (2026)

    2026

  25. [33]

    Zhang, Z

    K. Zhang, Z. Yang, and C. Fang, Correspondence between winding numbers and skin modes in non- Hermitian systems, Phys. Rev. Lett.125, 126402 (2020)

    2020

  26. [34]

    Okuma, K

    N. Okuma, K. Kawabata, K. Shiozaki, and M. Sato, Topological origin of non-Hermitian skin effects, Phys. Rev. Lett.124, 086801 (2020)

    2020

  27. [35]

    M. M. Denner, A. Skurativska, F. Schindler, M. H. Fis- cher, R. Thomale, T. Bzduˇ sek, and T. Neupert, Excep- tional topological insulators, Nat. Commun.12, 5681 (2021)

    2021

  28. [36]

    E. J. Bergholtz, J. C. Budich, and F. K. Kunst, Excep- tional topology of non-Hermitian systems, Rev. Mod. Phys.93, 015005 (2021)

    2021

  29. [37]

    Zhou and D.-J

    L. Zhou and D.-J. Zhang, Non-Hermitian Floquet topo- logical matter—a review, Entropy25, 1401 (2023)

    2023

  30. [38]

    Nakamura, T

    D. Nakamura, T. Bessho, and M. Sato, Bulk-boundary correspondence in point-gap topological phases, Phys. Rev. Lett.132, 136401 (2024)

    2024

  31. [39]

    G. K. Dash, S. Bid, and M. Thakurathi, Floquet excep- tional topological insulator, Phys. Rev. B109, 035418 (2024)

    2024

  32. [40]

    Tanaka, D

    Y. Tanaka, D. Nakamura, R. Okugawa, and K. Kawa- bata, Exceptional second-order topological insulators, Phys. Rev. B112, 245302 (2025)

    2025

  33. [41]

    Y. Sun, T. Shi, and Y. Hu, Anomalous point-gap in- teractions unveil the mirage bath, Phys. Rev. Res.7, 043231 (2025)

    2025

  34. [42]

    Chaduteau, D

    A. Chaduteau, D. K. K. Lee, and F. Schindler, Lindbla- dian versus postselected non-Hermitian topology, Phys. Rev. Lett.136, 016603 (2026)

    2026

  35. [43]

    Xue, Essay: Topological phases and exceptional points in non-Hermitian systems, Phys

    P. Xue, Essay: Topological phases and exceptional points in non-Hermitian systems, Phys. Rev. Lett.136, 170001 (2026)

    2026

  36. [44]

    C. H. Lee, L. Li, and J. Gong, Hybrid higher-order skin- topological modes in nonreciprocal systems, Phys. Rev. Lett.123, 016805 (2019)

    2019

  37. [45]

    C. H. Lee and R. Thomale, Anatomy of skin modes and topology in non-Hermitian systems, Phys. Rev. B99, 201103(R) (2019)

    2019

  38. [46]

    Okugawa, R

    R. Okugawa, R. Takahashi, and K. Yokomizo, Non- Hermitian band topology with generalized inversion symmetry, Phys. Rev. B103, 205205 (2021)

    2021

  39. [47]

    B. A. Bhargava, I. C. Fulga, J. van den Brink, and A. G. Moghaddam, Non-Hermitian skin effect of dislocations and its topological origin, Phys. Rev. B104, L241402 (2021)

    2021

  40. [48]

    Claes and T

    J. Claes and T. L. Hughes, Skin effect and winding num- ber in disordered non-Hermitian systems, Phys. Rev. B 103, L140201 (2021)

    2021

  41. [49]

    K. Xu, X. Zhang, K. Luo, R. Yu, D. Li, and H. Zhang, Coexistence of topological edge states and skin effects in the non-Hermitian Su-Schrieffer-Heeger model with long-range nonreciprocal hopping in topoelectric real- izations, Phys. Rev. B103, 125411 (2021)

    2021

  42. [50]

    Y. Li, C. Liang, C. Wang, C. Lu, and Y.-C. Liu, Gain- loss-induced hybrid skin-topological effect, Phys. Rev. Lett.128, 223903 (2022)

    2022

  43. [51]

    Zhu and J

    W. Zhu and J. Gong, Hybrid skin-topological modes without asymmetric couplings, Phys. Rev. B106, 035425 (2022)

    2022

  44. [52]

    He, Y.-G

    P. He, Y.-G. Liu, J.-T. Wang, and S.-L. Zhu, Damping transition in an open generalized Aubry-Andr´ e-Harper model, Phys. Rev. A105, 023311 (2022)

    2022

  45. [53]

    Wang, Z.-K

    L.-W. Wang, Z.-K. Lin, and J.-H. Jiang, Non-Hermitian topological phases and skin effects in kagome lattices, Phys. Rev. B108, 195126 (2023)

    2023

  46. [54]

    Wang, J.-S

    Z.-Y. Wang, J.-S. Hong, and X.-J. Liu, Symmetric non- Hermitian skin effect with emergent nonlocal correspon- dence, Phys. Rev. B108, L060204 (2023)

    2023

  47. [55]

    X.-R. Ma, K. Cao, X.-R. Wang, Z. Wei, Q. Du, and S.-P. Kou, Non-Hermitian chiral skin effect, Phys. Rev. Res.6, 013213 (2024)

    2024

  48. [56]

    K. Shi, L. Qiao, Z. Zheng, and W. Zhang, Floquet topo- logical phases and skin effects in periodically driven non- Hermitian systems, Phys. Rev. A110, 022222 (2024)

    2024

  49. [57]

    Yang and H

    W. Yang and H. Huang, Unified multipole bott indices for non-Hermitian skin effect in different orders, Phys. Rev. B111, 155121 (2025)

    2025

  50. [58]

    S. M. Rafi-Ul-Islam, Z. B. Siu, M. S. H. Razo, and M. B. A. Jalil, Critical non-Hermitian skin effect in a cross-coupled Hermitian chain, Phys. Rev. B111, 115415 (2025)

    2025

  51. [59]

    Cheng, Y

    D. Cheng, Y. Li, H. Zhao, H. Kang, C. Kong, J. Wang, F. Mei, C. Shan, and J. Liu, Maximal coin-position en- tanglement and non-Hermitian skin effect in discrete- time quantum walks, Phys. Rev. A112, 062205 (2025)

    2025

  52. [60]

    Sen and C

    G. Sen and C. Yuce, Edge burst effect and scale-free localization, Phys. Rev. B111, 174305 (2025)

    2025

  53. [61]

    Padlewski, R

    M. Padlewski, R. Fleury, and H. Lissek, Observation of amplitude-driven nonreciprocity for energy guiding, Phys. Rev. B111, 125156 (2025)

    2025

  54. [62]

    L. Zhou, R. Jing, and S. Wu, Topological characteri- zation of phase transitions and critical edge states in one-dimensional non-Hermitian systems with sublattice symmetry, Front. Phys.21, 075202 (2026)

    2026

  55. [63]

    Li and Q.-B

    P.-X. Li and Q.-B. Zeng, Tunable non-Hermitian skin effect and topological phases in ladders with staggered nonreciprocal inter-leg hopping (2026), arXiv:2607.11454 [quant-ph]

    2026 arXiv

  56. [64]

    Ma, M.-J

    Y.-P. Ma, M.-J. Gao, and J.-H. An, Topological phases in non-Hermitian nonlinear-eigenvalue systems, Phys. Rev. B113, L121401 (2026)

    2026

  57. [65]

    X. Ji, D. Wang, T. Zhou, and X. Yang, Non-Hermitian higher-order topological insulators enabled by altermag- net engineering, Phys. Rev. B113, 245420 (2026)

    2026

  58. [66]

    Yang and H

    W. Yang and H. Huang, Noise-induced revival of dy- namical skin effects in quasiperiodic non-hermitian sys- tems, Phys. Rev. B113, 174305 (2026)

    2026

  59. [67]

    J. M. Zeuner, M. C. Rechtsman, Y. Plotnik, Y. Lumer, S. Nolte, M. S. Rudner, M. Segev, and A. Szameit, Ob- servation of a topological transition in the bulk of a non-Hermitian system, Phys. Rev. Lett.115, 040402 (2015)

    2015

  60. [68]

    L. Xiao, T. Deng, K. Wang, G. Zhu, Z. Wang, W. Yi, and P. Xue, Non-Hermitian bulk–boundary correspon- dence in quantum dynamics, Nat. Phys.16, 761 (2020)

    2020

  61. [69]

    Hofmann, T

    T. Hofmann, T. Helbig, F. Schindler, N. Salgo, M. Brzezi´ nska, M. Greiter, T. Kiessling, D. Wolf, A. Vollhardt, A. Kabaˇ si, C. H. Lee, A. Biluˇ si´ c, R. Thomale, and T. Neupert, Reciprocal skin effect and its realization in a topolectrical circuit, Phys. Rev. Res. 2, 023265...

    2020

  62. [70]

    Zhang, Y

    X. Zhang, Y. Tian, J.-H. Jiang, M.-H. Lu, and Y.-F. Chen, Observation of higher-order non-Hermitian skin effect, Nat. Commun.12, 5377 (2021)

    2021

  63. [71]

    D. Zou, T. Chen, W. He, J. Bao, C. H. Lee, H. Sun, and X. Zhang, Observation of hybrid higher-order skin- topological effect in non-Hermitian topolectrical cir- cuits, Nat. Commun.12, 7201 (2021)

    2021

  64. [72]

    Liang, D

    Q. Liang, D. Xie, Z. Dong, H. Li, H. Li, B. Gad- way, W. Yi, and B. Yan, Dynamic signatures of non- Hermitian skin effect and topology in ultracold atoms, Phys. Rev. Lett.129, 070401 (2022)

    2022

  65. [73]

    Z. Gu, H. Gao, H. Xue, J. Li, Z. Su, and J. Zhu, Tran- sient non-Hermitian skin effect, Nat. Commun.13, 7668 (2022)

    2022

  66. [74]

    W. Wang, M. Hu, X. Wang, G. Ma, and K. Ding, Exper- imental realization of geometry-dependent skin effect in a reciprocal two-dimensional lattice, Phys. Rev. Lett. 131, 207201 (2023)

    2023

  67. [75]

    B. Liu, Y. Li, B. Yang, X. Shen, Y. Yang, Z. H. Hang, and M. Ezawa, Experimental observation of non- Hermitian higher-order skin interface states in topolog- ical electric circuits, Phys. Rev. Res.5, 043034 (2023)

    2023

  68. [76]

    Y. Sun, X. Hou, T. Wan, F. Wang, S. Zhu, Z. Ruan, and Z. Yang, Photonic Floquet skin-topological effect, Phys. Rev. Lett.132, 063804 (2024)

    2024

  69. [77]

    Jiang, C

    T. Jiang, C. Zhang, R.-Y. Zhang, Y. Yu, Z. Guan, Z. Wei, Z. Wang, X. Cheng, and C. T. Chan, Obser- vation of non-Hermitian boundary induced hybrid skin- topological effect excited by synthetic complex frequen- cies (2024), arXiv:2411.13221 [physics.optics]

    2024 arXiv

  70. [78]

    E. Zhao, Z. Wang, C. He, T. F. J. Poon, K. K. Pak, Y.-J. Liu, P. Ren, X.-J. Liu, and G.-B. Jo, Two-dimensional non-Hermitian skin effect in an ultracold Fermi gas, Na- ture637, 565 (2025)

    2025

  71. [79]

    J. Wu, Y. Hu, Z. He, K. Deng, X. Huang, M. Ke, W. Deng, J. Lu, and Z. Liu, Hybrid-order skin effect from loss-induced nonreciprocity, Phys. Rev. Lett.134, 176601 (2025)

    2025

  72. [80]

    R. Shen, T. Chen, B. Yang, and C. H. Lee, Observa- tion of the non-Hermitian skin effect and Fermi skin on a digital quantum computer, Nat. Commun.16, 1340 (2025)

    2025

  73. [81]

    S. Wang, J. He, Z. Yang, S. Longhi, and P. Xue, Non-Hermitian anomalous scaling engineering (2026), arXiv:2603.26175 [physics.optics]

    2026

  74. [82]

    S. Wang, W. Xiong, Z. Zhang, Y. Cheng, and X. Liu, One-dimensionalZ 2 topological skin effect driven by acoustic lossy couplings, Phys. Rev. Lett.136, 026601 (2026)

    2026

  75. [83]

    L. Liu, Y. Li, W. Wang, Q. Zhang, and C. Qiu, Obser- vation of higher-dimensional point-gap bulk-boundary correspondence, Phys. Rev. Lett.136, 166602 (2026)

    2026

  76. [84]

    Sirker, Pseudospectral phenomena and the origin of the non-Hermitian skin effect (2026), arXiv:2603.22643 [cond-mat.stat-mech]

    J. Sirker, Pseudospectral phenomena and the origin of the non-Hermitian skin effect (2026), arXiv:2603.22643 [cond-mat.stat-mech]

    2026 arXiv

  77. [85]

    Monkman and J

    K. Monkman and J. Sirker, Hidden Zero Modes and Topology of Multiband Non-Hermitian Systems, Phys. Rev. Lett.134, 056601 (2025)

    2025

  78. [86]

    Wu, X.-M

    H. Wu, X.-M. Yang, J. Li, and H. Liu, Instability of edge states and a singular-value-based diagnostic scheme for the topology in one-dimensional Floquet non-Hermitian systems, Phys. Rev. B113, 235123 (2026)

    2026

  79. [87]

    X.-M. Yang, H. Lin, J. Li, J.-J. Zhu, J.-L. Zhu, and H. Wu, Singular-value-based bulk-boundary correspon- dence in a separable non-Hermitian second-order topo- logical insulator, Phys. Rev. B113, 195138 (2026)

    2026

  80. [88]

    L. N. Trefethen and M. Embree,Spectra and Pseu- dospectra(Princeton University Press, 2005)

    2005

  81. [89]

    Sirker, Bulk-boundary correspondence in topological two-dimensional non-Hermitian systems: Toeplitz oper- ators and singular values, SciPost Phys.21, 013 (2026)

    J. Sirker, Bulk-boundary correspondence in topological two-dimensional non-Hermitian systems: Toeplitz oper- ators and singular values, SciPost Phys.21, 013 (2026)

    2026

  82. [90]

    X. Feng, S. Liu, S.-X. Zhang, and S. Chen, Numeri- cal instability of non-Hermitian Hamiltonian evolution, Phys. Rev. B111, 224310 (2025)

    2025

  83. [91]

    Zhang, L.-Z

    D.-W. Zhang, L.-Z. Tang, L.-J. Lang, H. Yan, and S.- L. Zhu, Non-Hermitian topological Anderson insulators, Sci. China Phys. Mech. Astron.63, 267062 (2020)

    2020

  84. [92]

    Agarwala, V

    A. Agarwala, V. Juriˇ ci´ c, and B. Roy, Higher-order topo- logical insulators in amorphous solids, Phys. Rev. Res. 2, 012067(R) (2020)

    2020

  85. [93]

    X. Luo, T. Ohtsuki, and R. Shindou, Universality classes of the Anderson transitions driven by non-Hermitian disorder, Phys. Rev. Lett.126, 090402 (2021)

    2021

  86. [94]

    C. C. Wanjura, M. Brunelli, and A. Nunnenkamp, Cor- respondence between non-Hermitian topology and di- rectional amplification in the presence of disorder, Phys. Rev. Lett.127, 213601 (2021)

    2021

  87. [95]

    Spring, A

    H. Spring, A. R. Akhmerov, and D. Varjas, Amor- phous topological phases protected by continuous ro- tation symmetry, SciPost Phys.11, 022 (2021)

    2021

  88. [96]

    Guzm´ an, D

    M. Guzm´ an, D. Bartolo, and D. Carpentier, Geometry and topology tango in ordered and amorphous chiral matter, SciPost Phys.12, 038 (2022)

    2022

  89. [97]

    Sarkar, S

    R. Sarkar, S. S. Hegde, and A. Narayan, Interplay of disorder and point-gap topology: Chiral modes, local- ization, and non-Hermitian Anderson skin effect in one dimension, Phys. Rev. B106, 014207 (2022)

    2022

  90. [98]

    S. Kim, A. Agarwala, and D. Chowdhury, Fractionaliza- tion and topology in amorphous electronic solids, Phys. Rev. Lett.130, 026202 (2023)

    2023

  91. [99]

    R. Qi, J. Cao, and X.-P. Jiang, Localization and mobil- ity edges in non-Hermitian disorder-free lattices (2023), arXiv:2306.03807 [cond-mat.dis-nn]

    2023 arXiv

  92. [100]

    Wang and X

    C. Wang and X. R. Wang, Anderson localization transi- tions in disordered non-Hermitian systems with excep- tional points, Phys. Rev. B107, 024202 (2023)

    2023

  93. [101]

    Zhang, H

    Z.-Q. Zhang, H. Liu, H. Liu, H. Jiang, and X. Xie, Bulk- boundary correspondence in disordered non-Hermitian systems, Science Bulletin68, 157–164 (2023)

    2023

  94. [102]

    J. D. Hannukainen, M. F. Mart ´ ınez, J. H. Bardar- son, and T. K. Kvorning, Local topological markers in odd spatial dimensions and their application to amor- phous topological matter, Phys. Rev. Lett.129, 277601 (2022)

    2022

  95. [103]

    Peng, C.-B

    T. Peng, C.-B. Hua, R. Chen, Z.-R. Liu, H.-M. Huang, and B. Zhou, Density-driven higher-order topological phase transitions in amorphous solids, Phys. Rev. B 106, 125310 (2022)

    2022

  96. [104]

    Corbae, J

    P. Corbae, J. D. Hannukainen, Q. Marsal, D. Mu˜ noz- Segovia, and A. G. Grushin, Amorphous topological matter: Theory and experiment, Europhysics Letters 142, 16001 (2023)

    2023

  97. [105]

    Tao, J.-H

    Y.-L. Tao, J.-H. Wang, and Y. Xu, Average symme- try protected higher-order topological amorphous insu- lators, SciPost Phys.15, 193 (2023)

    2023

  98. [106]

    D. Li, C. Wang, and H. Huang, Real-space approach for the Euler class and fragile topology in quasicrystals and amorphous lattices, SciPost Phys.17, 086 (2024). 9

    2024

  99. [107]

    He, J.-X

    P. He, J.-X. Liu, H. Wu, and Z. D. Wang, Floquet amor- phous topological orders in a one-dimensional Rydberg glass, Commun. Phys.8, 237 (2025)

    2025

  100. [108]

    A. K. Ghosh, Q. Marsal, and A. M. Black-Schaffer, Laser-induced topological phases in monolayer amor- phous carbon, Phys. Rev. B113, L121402 (2026)

    2026

  101. [109]

    E. T. Kokkinakis, I. Komis, K. G. Makris, and E. N. Economou, Non-Hermitian off-diagonal disordered op- tical lattices, Phys. Rev. B113, 174210 (2026)

    2026

  102. [110]

    Steinfurth, S

    A. Steinfurth, S. Weidemann, J. G¨ orsch, T. Shep- pard, H. M. Price, A. Szameit, and J. Feis, Disorder- immune momentum band winding topology (2026), arXiv:2604.10486 [physics.optics]

    2026 arXiv

  103. [111]

    Vanoni, J

    C. Vanoni, J. Karcher, M. C. Rechtsman, B. L. Alt- shuler, P. J. Steinhardt, and S. Torquato, Effective delo- calization in the one-dimensional Anderson model with stealthy disorder, Phys. Rev. Lett.136, 150404 (2026)

    2026

  104. [112]

    Komis, E

    I. Komis, E. T. Kokkinakis, K. G. Makris, and E. N. Economou, Evolving disorder in non-Hermitian lattices, Phys. Rev. Res.8, 023227 (2026)

    2026

  105. [113]

    Manna and B

    S. Manna and B. Roy, Inner skin effects on non- Hermitian topological fractals, Commun. Phys.6, 10 (2023)

    2023

  106. [114]

    Cheng, T

    S. Cheng, T. Liu, and G. Xianlong, Unbound states and mixed bound–unbound phases in near-infinitely deep potentials (2026), arXiv:2604.21281 [cond-mat.dis-nn]

    2026 arXiv

  107. [115]

    W.-W. Jin, J. Liu, X. Wang, Y.-R. Zhang, X. Huang, X. Wei, W. Ju, Z. Yang, T. Liu, and F. Nori, Ander- son delocalization in strongly coupled disordered non- Hermitian chains, Phys. Rev. Lett.135, 076602 (2025)

    2025

  108. [116]

    Herviou, J

    L. Herviou, J. H. Bardarson, and N. Regnault, Defining a bulk-edge correspondence for non-Hermitian hamilto- nians via singular-value decomposition, Phys. Rev. A 99, 052118 (2019)

    2019

  109. [117]

    Ashida, Z

    Y. Ashida, Z. Gong, and M. Ueda, Non-Hermitian physics, Advances in Physics69, 249–435 (2020)

    2020

  110. [118]

    L. Lin, Y. Ke, and C. Lee, Real-space representation of the winding number for a one-dimensional chiral- symmetric topological insulator, Phys. Rev. B103, 224208 (2021)

    2021

  111. [119]

    W. A. Benalcazar and A. Cerjan, Chiral-symmetric higher-order topological phases of matter, Phys. Rev. Lett.128, 127601 (2022)

    2022

  112. [120]

    Z. Lin, J. Li, W. Song, S. Su, J. Sun, S. Wu, C. Huang, S. Zhu, and T. Li, Dissipative topological dynamics in optical waveguides: Sensitivity versus robustness, Phys. Rev. Lett.134, 223802 (2025)

    2025

  113. [121]

    Zhang, S

    Z. Zhang, S. Liang, I. Septembre, J. Yu, Y. Huang, M. Liu, Y. Zhang, M. Xiao, G. Malpuech, and D. Solnyshkov, Non-Hermitian delocalization in a two- dimensional photonic quasicrystal, Phys. Rev. Lett. 132, 263801 (2024)

    2024

  114. [122]

    Zhang, Y.-J

    J. Zhang, Y.-J. Wang, S.-Y. Shao, B. Liu, L.-H. Zhang, Z.-Y. Zhang, X. Liu, C. Yu, Q. Li, H.-C. Chen, Y. Ma, T.-Y. Han, Q.-F. Wang, J.-D. Nan, Y.-M. Yin, D.-Y. Zhu, Q.-Q. Fang, D.-S. Ding, and B.-S. Shi, Observation of non-Hermitian topology in cold Rydberg quantum gases (2025...

    2025

  115. [123]

    Naghiloo, M

    M. Naghiloo, M. Abbasi, Y. N. Joglekar, and K. W. Murch, Quantum state tomography across the excep- tional point in a single dissipative qubit, Nat. Phys.15, 1232–1236 (2019)

    2019

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