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REVIEW 4 major objections 5 minor 64 references

Non-Hermitian second-order topological insulator with point gap

T0 review · 4 major / 5 minor · reviewed 2026-08-03 · deepseek-v4-flash

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Pith's one-line read This paper claims that even when disorder destroys the corner-state energies of a non-Hermitian higher-order topological insulator, the zero singular values of the Hamiltonian still count the topologically protected corner states in the the

desk verdict Useful Floquet SVD proposal, but the central singular-value/energy correspondence is asserted rather than proved, and the authors' own data hint at a real discrepancy. read the letter →

arxiv 2601.01524 v1 pith:KQLVAGAJ submitted 2026-01-04 quant-ph

Xue-Min Yang , Hao Lin , Jian Li , Jia-Ji Zhu , Jun-Li Zhu , Hong Wu This is my paper
classification quant-ph
keywords non-Hermitiantopologicalinsulatorhigher-ordertopologysingularvaluespectrumbulk-boundarycorrespondencecornerstatesFloquetphasespointgapskineffect
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 two-dimensional non-Hermitian Su-Schrieffer-Heeger model whose corner-state energies are destroyed by arbitrarily weak disorder, even disorder that preserves chiral symmetry, because the Hamiltonian is far from normal. It argues that the stable topological content is not in the energy eigenvalues but in the singular-value spectrum: the number of zero-mode singular values equals $2V$, a real-space winding number, and this count remains intact under perturbations that destroy the spectral corner states. In the thermodynamic limit, each zero singular value corresponds to a topologically protected corner state. The same construction applies to Floquet systems, where singular values of $U(T)-I$ and $U(T)+I$ count 0- and π-modes.

What carries the argument

The central object is the singular-value decomposition of the non-Hermitian Hamiltonian, $H_{2D} = U S V^\dagger$, together with the associated Hermitian chiral-symmetric matrix $\tilde{H} = \begin{bmatrix} 0 & H \\ H^\dagger & 0 \end{bmatrix}$, whose eigenvalues are $\pm s_n$. Singular values $s_n$ are real, non-negative, and stable under perturbation, unlike the complex eigenvalues of a non-normal operator. A real-space winding number $V$, computed from the unitary factors $U$ and $V$ via a diagonal twist matrix $P$, counts the number $2V$ of zero singular values and therefore the number of protected corner states.

What would settle it

At the parameter point of Fig. 2(b) ($w_x = 1$, $v_x = -1.5$, $\gamma_x = 1.5$, $w_y = 0$, $v_y = -9$, $\gamma_y = 9$, system sizes growing up to $1000 \times 1000$), compute the smallest singular vector $v$ of $H_{2D}$ with singular value $s$, and evaluate $\|H_{2D} v\|/s$ as a function of size. If this ratio grows without bound while $s$ decays, the singular vector is not approaching a zero-energy eigenstate, and the claimed correspondence between zero singular values and corner eigenstates would fail.

Watch

Extended reading notes

Core claim

The central claim is that for a non-Hermitian Hamiltonian $H_{2D}$ with a point gap at $E=0$, the number of zero singular values of $H_{2D}$ — equivalently the zero eigenvalues of the Hermitian doubled matrix $\tilde{H} = \begin{bmatrix} 0 & H \\ H^\dagger & 0 \end{bmatrix}$ — is exactly $2V$, where $V$ is a winding number computed from the SVD singular vectors via $P_A = U^\dagger P U$, $P_B = V^\dagger P V$. This number counts topologically protected corner states of the energy spectrum in the thermodynamic limit, and it survives both chiral-symmetric and fully symmetry-breaking disorder, in contrast to the fragile energy eigenvalues whose gaps are destroyed even by infinitesimal perturbations. The same logic applies to Floquet systems by replacing $H$ with $U(T)-I$

Load-bearing premise

A singular vector with a vanishing singular value in a finite open-boundary system is assumed to converge to an actual zero-energy corner eigenstate in the thermodynamic limit, even though for a non-normal Hamiltonian a zero singular value does not by itself guarantee a zero eigenstate.

Editorial extensions

If this is right

  • If the correspondence holds, the number of protected corner states in a non-Hermitian higher-order topological insulator is given by the singular-value winding number 2V, not by the non-Bloch invariant, resolving the breakdown of bulk-boundary correspondence.
  • The invariant is robust to disorder that breaks chiral symmetry, so topological corner states can be certified without requiring symmetry protection.
  • In Floquet systems, 0- and π-modes are characterized by zero singular values of U(T)−I and U(T)+I, respectively, giving direct counting invariants V− and V+.
  • The exponential decay of the smallest singular value with system size provides a finite-size scaling tool for identifying topological phases in numerical and experimental data.

Reading between the lines

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

  • Because zero singular values of a non-normal operator do not generally imply zero eigenstates, the paper's mapping from singular vectors to corner states in the thermodynamic limit is an assumption that would need a separate proof for generic non-Hermitian Hamiltonians; the paper's numerical evidence suggests it, but no general theorem is established.
  • The method suggests a practical experimental protocol: measure the response matrix or scattering matrix of a finite lattice and inspect its singular values, rather than attempting to resolve fragile complex spectra, to detect higher-order topology.
  • If the singular-value winding number is the correct invariant, it may generalize to other non-Hermitian topological phases with point-gap topology, providing a classification scheme based on SVD rather than on generalized Brillouin zones.
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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

4 major / 5 minor

Summary. The manuscript studies a two-dimensional non-Hermitian Su-Schrieffer-Heeger model and its Floquet-driven variant. It first shows that the conventional non-Bloch winding-number prediction of zero-energy corner states breaks down under weak chiral-preserving disorder in large systems, attributing the instability to the large condition number of the nonnormal Hamiltonian. It then proposes to restore a bulk-boundary correspondence using the singular-value spectrum of H2D (and U(T)±I for Floquet systems), defines a real-space winding number V (resp. V±), and claims that the number of zero-mode singular values equals 2V (resp. 2V±) and directly counts topologically protected corner states of the energy spectrum in the thermodynamic limit.

Significance. If the central correspondence were valid, the paper would provide a stable way to identify higher-order topological boundary states in non-Hermitian systems, going beyond fragile non-Bloch invariants. The observation that energy zero modes are unstable while singular values are stable is a useful and interesting numerical fact, and the Floquet extension is natural. However, the claimed equivalence between zero singular values and zero-energy eigenstates is not proved and, as stated, is not valid for nonnormal operators. Since this equivalence is the load-bearing step of the paper, the significance of the results for energy-spectrum topology is not established.

major comments (4)
  1. [§3, Eqs. (7)-(8)] The inference from s_n→0 to 'the system supports zero-mode states with wave function v_n' is invalid for nonnormal H. For example, M=[[0,R],[1/R,0]] has singular values R and 1/R, so the smallest singular value tends to 0 as R→∞, while the eigenvalues remain ±1. The reported condition number κ=2.93×10^9 in Eq. (6) places the model precisely in the regime where eigenvalues and singular values differ strongly. The contrast between Fig. 2(b), where Min|E| leaves zero under chiral-preserving disorder, and Fig. 3(a), where Min[s] is plotted as zero for the same type of weak disorder, is direct evidence that the singular-value spectrum is not equivalent to the eigenvalue spectrum. A proof that the singular vectors converge to genuine zero-energy eigenstates of H2D in the thermodynamic limit for this model is required before the central claim can be accepted.
  2. [§3, Eq. (10) and following] The equality 'number of zero-mode singular values equals 2V' is presented as a new bulk-boundary correspondence, but V is computed from the same open-boundary SVD (U and V in Eq. (11)) whose zero singular values are being counted. The construction via the doubled Hermitian operator H̃ in Eq. (9) is the standard chiral-index argument from Refs. [49,51], so the equality is at least partly a restatement of the index theory of H̃ rather than an independent correspondence between singular states and energy eigenstates. The manuscript should specify whether V is a bulk quantity obtained from periodic-boundary data and should provide the index-theoretic derivation step by step.
  3. [§3, Fig. 3(a)] For a finite matrix with fully random, symmetry-breaking disorder, no exact zero singular value is expected generically. The plotted 'Min[s]=0' therefore relies on an unspecified numerical threshold. Without a precise threshold, the count of zero-mode singular values is not well defined, and the claimed equality with 2V cannot be tested. The same issue affects Fig. 4 for the singular values of U(T)±I.
  4. [§3, Fig. 3(b) and thermodynamic limit] The paper demonstrates exponential decay of Min[s] with system size, but the claimed correspondence is to energy corner states in the thermodynamic limit. It does not provide the analogous scaling of Min|E| for the same disordered systems; the finite-size data in Fig. 2(b) suggest that Min|E| remains finite. Thus the thermodynamic-limit statement about energy eigenstates is not supported by the numerical evidence presented.
minor comments (5)
  1. [§3, text after Eq. (8)] Typo: 'mordynamic' should be 'thermodynamic'.
  2. [§3, Fig. 3(a) caption] Typo: 'ia also equal' should be 'is also equal'.
  3. [Eq. (3)] The notation C̃_k for the generalized Brillouin zone is not defined precisely; the orientation of the contour and the branch of the logarithm should be specified.
  4. [Eq. (5)] The weighted inverse participation ratio formula appears to lack a normalization factor and a clear summation convention; the present expression is not dimensionless as written.
  5. [Eq. (10)] The expression Tr ln(PA PB†) should be defined with a statement about the branch of the logarithm and why the result is quantized; as written the reader must infer the intended convention.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the SVD-to-energy correspondence is a rigor gap, not a circular reduction.

full rationale

The central claim is not circular by the definitions used here. The real-space winding V (Eq. 10) is computed from the SVD singular vectors U,V and the position operator P, not from the singular values themselves, so the zero-singular-value count is not fitted into V. The equality 'number of zero-mode singular values = 2V' rests on the index theory of the chiral doubled operator H̃ (Eqs. 9-10), with the needed bulk-edge/index correspondence imported from external references [49,51], which are not authored by the present group. The only self-citation, ref. [46], motivates the instability of non-Bloch invariants but is not load-bearing: this paper independently demonstrates that instability in Fig. 2(b). The main weakness in the derivation is the inference from s_n→0 (Eqs. 7-8) to 'zero-mode states with wave function v_n' of H2D; for a highly non-normal operator (κ=2.93×10^9), small singular values do not guarantee small eigenvalues. That is an unproven physical correspondence or mathematical rigor problem, not a reduction of the prediction to its inputs. The paper neither fits V nor defines it in terms of the singular-value count, so no step reduces by construction to its own input.

Assumptions & free parameters 1 free parameters · 3 assumptions · 0 invented entities

The paper pulls two major structural ingredients from prior literature: SVD-based edge correspondence (ref [49]) and real-space chiral winding numbers (ref [51]). It contributes a new combination and a Floquet extension, but neither the index theorem nor the thermodynamic-limit correspondence is derived here. No free parameters are fitted to data beyond the illustrative Hamiltonian parameters.

free parameters (1)
  • Exemplar NH SSH parameters (w_x=1, w_y=0, γ_x=1.5, γ_y=9 or 10.5, v_y=6 or 7 v_x, T=0.6, q=0.2) = Hand-chosen values used in Figs. 2-4
    The numerical demonstration of the bulk-boundary correspondence is restricted to these hand-picked parameters; the paper does not show that the singular-value count equals the corner-state count for generic parameter settings.
assumptions (3)
  • domain assumption A zero singular value of H2D (s_n→0) implies a zero-energy corner eigenstate in the thermodynamic limit; H2D v_n = s_n u_n → 0 does not by itself make v_n an eigenstate for a non-normal H.
    Eqs. (7)-(8) and Fig. 3(b) use exponential decay of Min[s] to infer protected corner states; because the Hamiltonian is far from normal (κ=2.93×10^9), singular vectors need not be eigenvectors, so this inference is nontrivial and unproven.
  • standard math The doubled Hermitian operator H̃ of Eq. (9) is chiral-symmetric, and the real-space winding number V of Eq. (10) counts its zero modes, giving 'number of zero singular values = 2V'.
    Imported from refs [49,51]; not proved here. This is the mathematical core of the claimed bulk-boundary correspondence.
  • domain assumption For Floquet systems, the singular values of U(T)−I and U(T)+I detect 0- and π-quasienergy modes, and the winding numbers V± of Eq. (16) count them.
    Eqs. (15)-(16) and Fig. 4 assert this by analogy with the static case; no derivation or proof is provided.

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Cite this review

Pith. "Pith review of Non-Hermitian second-order topological insulator with point gap." pith.science (2026). https://pith.science/paper/KQLVAGAJ

@misc{pith2026260101524,
  author       = {Pith},
  title        = {Pith review of: Non-Hermitian second-order topological insulator with point gap},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KQLVAGAJ}},
  note         = {Machine review of arXiv:2601.01524}
}
read the original abstract

The zero-mode corner states in the gap of two-dimensional non-Hermitian Su-Schrieffer-Heeger model are robust to infinitesimal perturbations that preserve chiral symmetry. However, we demonstrate that this general belief is no longer valid in large-sized systems. To reveal the higher-order topology of non-Hermitian systems, we establish a correspondence between the stable zero-mode singular states and the topologically protected corner states of energy spectrum in the thermodynamic limit. Within this framework, the number of zero-mode singular values is directly linked to the number of mid-gap corner states. The winding numbers in real space can be defined to count the number of stable zero-mode singular states. Our results formulate a bulk-boundary correspondence for both static and Floquet non-Hermitian systems, where topology arises intrinsically from the non-Hermiticity, even without symmetries.

Figures

Figures reproduced from arXiv: 2601.01524 by the authors.

Figure 2
Figure 2. FIG. 2. (a) The minimum modulus of the energy eigenval [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. (a) The smallest singular value (Min[ [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. FIG. 4. (a-b) The smallest singular values Min[ [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗

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Works this paper leans on

64 extracted references · 3 linked inside Pith

  1. [49]

    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. A99, 052118 (2019)

    2019

  2. [51]

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

    2022

  3. [1]

    M. Z. Hasan and C. L. Kane, Colloquium: Topological insulators, Rev. Mod. Phys.82, 3045 (2010)

    2010

  4. [2]

    Ozawa, H

    T. Ozawa, H. M. Price, A. Amo, N. Goldman, M. Hafezi, L. Lu, M. C. Rechtsman, D. Schuster, J. Simon, O. Zil- berberg, and I. Carusotto, Topological photonics, Rev. Mod. Phys.91, 015006 (2019)

    2019

  5. [3]

    N. R. Cooper, J. Dalibard, and I. B. Spielman, Topo- logical bands for ultracold atoms, Rev. Mod. Phys.91, 015005 (2019)

    2019

  6. [4]

    B. Q. Lv, T. Qian, and H. Ding, Experimental perspec- tive on three-dimensional topological semimetals, Rev. Mod. Phys.93, 025002 (2021)

    2021

  7. [5]

    C.-K. Chiu, J. C. Y. Teo, A. P. Schnyder, and S. Ryu, Classification of topological quantum matter with sym- metries, Rev. Mod. Phys.88, 035005 (2016)

    2016

  8. [6]

    W. A. Benalcazar, B. A. Bernevig, and T. L. Hughes, Quantized electric multipole insulators, Science357, 61–66 (2017)

    2017

Show all 64 references
  1. [7]

    Liu and K

    F. Liu and K. Wakabayashi, Novel topological phase with a zero Berry curvature, Phys. Rev. Lett.118, 076803 (2017)

    2017

  2. [8]

    Ezawa, Topological switch between second-order topological insulators and topological crystalline insula- tors, Phys

    M. Ezawa, Topological switch between second-order topological insulators and topological crystalline insula- tors, Phys. Rev. Lett.121, 116801 (2018)

    2018

  3. [9]

    Wang, Y.-B

    J.-H. Wang, Y.-B. Yang, N. Dai, and Y. Xu, Structural- disorder-induced second-order topological insulators in three dimensions, Phys. Rev. Lett.126, 206404 (2021)

    2021

  4. [10]

    Trifunovic and P

    L. Trifunovic and P. W. Brouwer, Higher-order bulk- boundary correspondence for topological crystalline phases, Phys. Rev. X9, 011012 (2019)

    2019

  5. [11]

    Chen, C.-Z

    R. Chen, C.-Z. Chen, J.-H. Gao, B. Zhou, and D.-H. Xu, Higher-order topological insulators in quasicrystals, Phys. Rev. Lett.124, 036803 (2020)

    2020

  6. [12]

    Schindler, A

    F. Schindler, A. M. Cook, M. G. Vergniory, Z. Wang, S. S. P. Parkin, B. A. Bernevig, and T. Neupert, Higher-order topological insulators, Science Advances4, eaat0346 (2018)

    2018

  7. [13]

    C. Chen, L. Qi, Y. Xing, W.-X. Cui, S. Zhang, and H.-F. Wang, General bounded corner states in two-dimensional off-diagonal Aubry–Andr´ e–Harper model with flat bands, New Journal of Physics23, 123008 (2021)

    2021

  8. [14]

    Xiong, Y

    Z. Xiong, Y. Liu, Z.-K. Lin, Z.-L. Kong, and J.-H. Jiang, Triband higher-order topological insulators, Phys. Rev. Appl.24, 024049 (2025)

    2025

  9. [15]

    J. Xiao, Q. Hu, Z. Yu, W. Chen, and X. Luo, Magnetic flux induced higher-order topological superconductivity, Phys. Rev. B112, 195404 (2025)

    2025

  10. [16]

    W. Jia, Y. Tian, H. Yang, X. Kong, Z.-H. Huang, W.-J. Gong, and J.-H. An, Unconventional hybrid-order topo- logical insulators, Phys. Rev. B112, L241103 (2025)

    2025

  11. [17]

    Chen, W.-M

    X.-D. Chen, W.-M. Deng, F.-L. Shi, F.-L. Zhao, M. Chen, and J.-W. Dong, Direct observation of corner states in second-order topological photonic crystal slabs, Phys. Rev. Lett.122, 233902 (2019)

    2019

  12. [18]

    Cerjan, M

    A. Cerjan, M. J¨ urgensen, W. A. Benalcazar, S. Mukher- jee, and M. C. Rechtsman, Observation of a higher-order topological bound state in the continuum, Phys. Rev. Lett.125, 213901 (2020)

    2020

  13. [19]

    Zhang, D

    W. Zhang, D. Zou, Q. Pei, W. He, J. Bao, H. Sun, and X. Zhang, Experimental observation of higher-order topological Anderson insulators, Phys. Rev. Lett.126, 146802 (2021)

    2021

  14. [20]

    D. Wang, Y. Deng, J. Ji, M. Oudich, W. A. Benal- cazar, G. Ma, and Y. Jing, Realization of aZ-classified chiral-symmetric higher-order topological insulator in a coupling-inverted acoustic crystal, Phys. Rev. Lett.131, 157201 (2023)

    2023

  15. [21]

    Z. Dong, H. Li, H. Wang, Y. Pan, W. Yi, and B. Yan, Observation of higher-order topological bound states in the continuum using ultracold atoms (2025), arXiv:2501.13499 [cond-mat.quant-gas]

    2025 arXiv

  16. [22]

    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

  17. [23]

    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

  18. [24]

    Jangjan, L

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

    2024

  19. [25]

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

    2019

  20. [26]

    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

  21. [27]

    Jezequel and P

    L. Jezequel and P. Delplace, Non-Hermitian spectral 6 flows and Berry-Chern monopoles, Phys. Rev. Lett.130, 066601 (2023)

    2023

  22. [28]

    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

  23. [29]

    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

  24. [30]

    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

  25. [31]

    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

  26. [32]

    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

  27. [33]

    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

  28. [34]

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

    2025 arXiv

  29. [35]

    Longhi, Erratic non-Hermitian skin localization, Phys

    S. Longhi, Erratic non-Hermitian skin localization, Phys. Rev. Lett.134, 196302 (2025)

    2025

  30. [36]

    Zhang, Z

    K. Zhang, Z. Yang, and K. Sun, Edge theory of non- Hermitian skin modes in higher dimensions, Phys. Rev. B109, 165127 (2024)

    2024

  31. [37]

    Shi and A

    J. Shi and A. N. Poddubny, Chiral dissociation of bound photon pairs for a non-Hermitian skin effect, Phys. Rev. Lett.134, 233602 (2025)

    2025

  32. [38]

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

    2016

  33. [39]

    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

  34. [40]

    Yokomizo and S

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

    2019

  35. [41]

    Wu and J.-H

    H. Wu and J.-H. An, Floquet topological phases of non- Hermitian systems, Phys. Rev. B102, 041119 (2020)

    2020

  36. [42]

    Liu, Y.-R

    T. Liu, Y.-R. Zhang, Q. Ai, Z. Gong, K. Kawabata, M. Ueda, and F. Nori, Second-order topological phases in non-Hermitian systems, Phys. Rev. Lett.122, 076801 (2019)

    2019

  37. [43]

    Zhang, M

    Z. Zhang, M. Rosendo L´ opez, Y. Cheng, X. Liu, and J. Christensen, Non-Hermitian sonic second-order topo- logical insulator, Phys. Rev. Lett.122, 195501 (2019)

    2019

  38. [44]

    Pan and L

    J. Pan and L. Zhou, Non-Hermitian Floquet second order topological insulators in periodically quenched lattices, Phys. Rev. B102, 094305 (2020)

    2020

  39. [45]

    Monkman and J

    K. Monkman and J. Sirker, Hidden zero modes and topol- ogy of multiband non-Hermitian systems, Phys. Rev. Lett.134, 056601 (2025)

    2025

  40. [46]

    Wu, X.-M

    H. Wu, X.-M. Yang, and H. Liu, Breakdown of non-Bloch bulk-boundary correspondence and emergent topology in Floquet non-Hermitian systems (2025), arXiv:2510.09193 [quant-ph]

    2025 arXiv

  41. [47]

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

    2005

  42. [48]

    Jing, J.-J

    Y. Jing, J.-J. Dong, Y.-Y. Zhang, and Z.-X. Hu, Biorthogonal dynamical quantum phase transitions in non-Hermitian systems, Phys. Rev. Lett.132, 220402 (2024)

    2024

  43. [50]

    Ashida, Z

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

    2020

  44. [52]

    Kundu, H

    A. Kundu, H. A. Fertig, and B. Seradjeh, Effective theory of Floquet topological transitions, Phys. Rev. Lett.113, 236803 (2014)

    2014

  45. [53]

    P. M. Perez-Piskunow, G. Usaj, C. A. Balseiro, and L. E. F. F. Torres, Floquet chiral edge states in graphene, Phys. Rev. B89, 121401 (2014)

    2014

  46. [54]

    Roy and F

    R. Roy and F. Harper, Periodic table for Floquet topo- logical insulators, Phys. Rev. B96, 155118 (2017)

    2017

  47. [55]

    Y. T. Katan and D. Podolsky, Modulated Floquet topo- logical insulators, Phys. Rev. Lett.110, 016802 (2013)

    2013

  48. [56]

    S.-Y. Bai, C. Chen, H. Wu, and J.-H. An, Quantum con- trol in open and periodically driven systems, Advances in Physics: X6, 1870559 (2021)

    2021

  49. [57]

    Ghuneim and R

    M. Ghuneim and R. W. Bomantara, Anomalous topo- logical edge modes in a periodically driven trimer lattice, Phys. Rev. B111, 195424 (2025)

    2025

  50. [58]

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

    2024

  51. [59]

    Xiao, W.-T

    L. Xiao, W.-T. Xue, F. Song, Y.-M. Hu, W. Yi, Z. Wang, and P. Xue, Observation of non-Hermitian edge burst in quantum dynamics, Phys. Rev. Lett.133, 070801 (2024)

    2024

  52. [60]

    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

  53. [61]

    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 (202...

    2025

  54. [62]

    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

  55. [63]

    W. Zhu, H. Xue, J. Gong, Y. Chong, and B. Zhang, Time- periodic corner states from Floquet higher-order topol- ogy, Nature Communications13, 11 (2022)

    2022

  56. [64]

    S.-Y. Shao, Q. Li, H.-C. Chen, B.-S. Shi, and D.-S. Ding, Higher-order and fractional discrete time crystals in floquet-driven rydberg atoms, Nature Communica- tions17, 9730 (2024)

    2024

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Reviewed August 3, 2026 · model on record in the stance chip above.