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Dynamically stable topological edge states in an extended Su-Schrieffer-Heeger ladder with balanced perturbation

T0 review · 2 major / 3 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read Balanced imaginary hopping and staggered potential can exactly preserve a spectrum while turning topological edge states into self-healing coalescing modes.

desk verdict Clean exact spectral result with an unsupported robustness claim; worth refereeing but needs softer wording and a local-disorder check. read the letter →

arxiv 2506.05666 v1 pith:6ZTKEMYV submitted 2025-06-06 cond-mat.str-el

E. S. Ma , K. L. Zhang , Z. Song This is my paper
classification cond-mat.str-el
keywords non-HermitiantopologicalphasesexceptionalpointsSu-Schrieffer-Heegerladdercoalescingedgestatessublatticewindingnumberbalancedperturbationdynamicalstabilitybulk-boundarycorrespondence
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 tries to establish that a non-Hermitian perturbation can counteract a symmetry-breaking on-site potential so completely that the system's energy spectrum is unchanged, while the character of its topological edge states is upgraded. In a class of bipartite lattices, an imaginary hopping of strength $i\gamma$ paired with a staggered potential $\pm V$ leaves the spectrum exactly that of the Hermitian lattice when $V=\pm\gamma$. In the extended Su-Schrieffer-Heeger ladder, the zero-energy edge states then become coalescing exceptional-point states, and time evolution drives a generic initial state into one of these stable edge states. The reason to care is that these edge states remain localized and self-recovering even when the system is temporarily quenched out of its topological phase, which points toward time-domain-stable topological devices.

What carries the argument

The engine is a block reduction of $H$ into independent $2\times2$ sectors. Because the intersublattice hopping matrix $T$ is antisymmetric, diagonalizing $iT$ gives $N$ pairs of modes with energies $\pm E_n$, and in that basis each pair is governed by a $2\times2$ matrix $M_n$ with diagonal entries $E_n$ and $-E_n$ and off-diagonal entries $V+\gamma$ and $V-\gamma$. Its eigenvalues are $\pm\sqrt{E_n^2+V^2-\gamma^2}$, so setting $V=\pm\gamma$ makes the spectrum identical to $H_0$'s, while setting $E_n^2=\gamma^2-V^2$ makes $M_n$ nilpotent, meaning its square vanishes. At that nilpotent point the two eigenstates coalesce, and time evolution contains a term linear in $t$ that steers the normalized state toward the coalescing mode. This is the mechanism the paper calls exceptional-point dynamics, and it is what turns ordinary edge states into dynamically stable ones.

What would settle it

Compute the spectrum of the ladder at $V=\gamma+\varepsilon$ with $\varepsilon\neq0$: the edge-state energies become $\pm\sqrt{2\gamma\varepsilon+\varepsilon^2}$, so the zero-energy coalescence is replaced by a measurable split pair. A numerical diagonalization at fixed $\delta>0$ would immediately show whether the claimed spectrum identity between $H$ and $H_0$ holds only at exact balance.

Watch

Extended reading notes

Core claim

The central claim, stated on the paper's own terms, is that the non-Hermitian Hamiltonian $H=H_0+H_p$ has exactly the spectrum of its Hermitian counterpart $H_0$ whenever the staggered potential $V$ and the imaginary hopping strength $\gamma$ are balanced, $V=\pm\gamma$. Under that condition each two-level subspace of $H$ takes a defective (Jordan-block) form, so the zero modes of $H_0$ cease to be two degenerate eigenstates and instead coalesce into single exceptional-point states. For the extended SSH ladder the authors show that the sublattice winding number remains quantized and the bulk-boundary correspondence holds: when the dimerization $\delta>0$, two edge states are localized at each end, and at $V=\gamma$ these edge states coalesce in pairs. Numerical time evolution demonstrates that a point-like or random initial state converges to a stable edge state, and a global quench of $\delta$ from $0.2$ to $-0.2$ disrupts the edge state only until the system is switched back, after which it recovers.

Load-bearing premise

The central construction requires the staggered potential and the imaginary hopping to be exactly balanced ($V=\pm\gamma$); if the balance is broken the spectrum identity disappears, and the dynamical convergence statement additionally assumes that the initial state has a non-vanishing component in the direction that activates the exceptional-point linear growth.

Editorial extensions

If this is right

  • For the extended SSH ladder with $\delta>0$, the sublattice winding number is $w^A=2$, so two edge states are localized at each end; this bulk-boundary correspondence is preserved despite the non-Hermitian perturbation.
  • At $V=\gamma$, an initially localized or random state evolves under normalized non-Hermitian time evolution into a stable coalescing edge state rather than spreading into the bulk.
  • The edge states are insensitive to a temporary quench into the trivial phase ($\delta<0$): numerical evolution shows the edge state is disrupted during the quench and recovers afterward, so the stability holds in the time domain.
  • Exceptional points are tunable through $\gamma$ and $V$, and the same coalescence can be induced for bulk eigenpairs, not only for the zero-energy edge states.
  • Because $H$ is pseudo-Hermitian, its spectrum is real or comes in complex-conjugate pairs, so the system keeps a line gap and does not develop the non-Hermitian skin effect.

Reading between the lines

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

  • Beyond the paper: the same $2\times2$ block argument applies to any bipartite lattice with an antisymmetric inter-sublattice hopping matrix, so the balanced-perturbation construction should generate dynamically stable coalescing states in other lattice geometries, not only the SSH ladder.
  • Beyond the paper: since the convergence mechanism is a Jordan-block linear-in-time growth rather than gain or loss, the effect should be reproducible in classical wave systems, such as coupled waveguides, acoustic lattices, or electrical circuits, where complex hoppings and staggered site energies can be engineered directly.
  • Testable extension: the quench-and-recovery simulation can serve as a quantitative self-healing probe by measuring the return time of the edge-state overlap as a function of the duration of the trivial-phase excursion.
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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

2 major / 3 minor

Summary. The manuscript studies a class of non-Hermitian bipartite tight-binding Hamiltonians H = H0 + Hp, where Hp is a balanced perturbation consisting of a staggered on-site potential ±V and an imaginary inter-sublattice hopping iγ. It proves exactly that when V = ±γ, the spectrum of H coincides with that of the Hermitian H0 (Eq. 14), and the zero modes of H0 become coalescing modes located at exceptional points of H. The paper then applies this formalism to an extended SSH ladder, computes the sublattice winding number, solves the edge states exactly in Appendix B, and shows numerically that generic initial states converge under normalized time evolution to the coalescing edge states (Eq. 16 and Fig. 2). A global quench of the dimerization parameter δ is also used to argue for time-domain robustness (Fig. 3). The abstract and conclusion further claim robustness against local perturbations and that a trivial initial state can always evolve to a stable edge state.

Significance. If the claims are properly qualified, the paper provides a useful exact construction: a parameter-free family of non-Hermitian lattice models whose spectrum is pinned to that of an underlying Hermitian model under a global balance condition, with analytically solvable coalescing edge states and an explicit exceptional-point dynamics mechanism for preparing them. The analytic edge-state solution agrees with the sublattice winding-number count, so the bulk-boundary correspondence statement is well supported for the clean, balanced model. The main advertised advantage over the ordinary SSH chain, namely robustness against local perturbations, is not established and is in tension with the global-balance requirement on which the exact spectral identity and the Jordan-block dynamics rely.

major comments (2)
  1. [Abstract and Sec. IV, Eq. (16)] The abstract's statement that a trivial initial state can 'always' evolve to a stable edge state is stronger than the derivation supports. According to Eq. (16), convergence to the coalescing mode requires that the initial state have a nonzero component in the non-coalescing direction, i.e., α ≠ E_{n'}β/(V−γ) for the relevant n' block. If the initial state is exactly the coalescing mode, or has zero overlap with the beta direction, the linear-in-time growth responsible for the normalization-driven convergence does not occur. The claim should be qualified to generic initial states satisfying this condition.
  2. [Sec. IV, Fig. 3; Abstract and Conclusion] The advertised robustness against local perturbations is neither demonstrated nor derived. The only numerical perturbation considered in the manuscript is a global quench of δ in Fig. 3, which preserves the uniform balance V = γ. A local perturbation, such as changing V on a single site, breaks the global balance V = ±γ on which both the spectral identity in Eq. (14) and the 2×2 Jordan-block dynamics in Eq. (16) rely; the block decomposition of Sec. II then no longer applies, the edge-state energy generally shifts away from zero, and the normalization-driven convergence to a single coalescing mode is destroyed. Because the model lacks chiral symmetry, the sublattice winding number computed in Sec. III B is not a symmetry-protected invariant that would guarantee robustness against arbitrary local disorder. The authors should either provide local-disorder simulations supporting the claim or remove and qualify the local-robustness assertion.
minor comments (3)
  1. [Sec. II, Eqs. (13) and (15)] The operator notation in Eqs. (13) and (15) is inconsistent: Eq. (13) writes H as a sum of terms E_{n,ρ} D_{n,ρ} D_{n,ρ}, whereas the first line of Eq. (15) defines D_{n,±} as a linear combination of the creation operators D†_{n,±}; as written, the expression in Eq. (13) looks like a product of two creation-like operators rather than the expected biorthogonal normal-ordered form H = Σ E_{n,ρ} D†_{n,ρ} D_{n,ρ}. Please correct the dagger placement and clarify the biorthogonal convention.
  2. [Sec. III B] The choice of reference energy ε = ±√(V² − γ²) in Eq. (33) is introduced without explanation; since this is also the edge-state energy in Eq. (39), a sentence connecting these two points would improve the readability of the bulk-boundary correspondence argument.
  3. [Appendix B] The word 'detials' in the first sentence of Appendix B should be 'details'.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the spectral identity and edge-state count are derived in-paper; remaining caveats are accuracy/robustness, not circularity.

full rationale

The central derivations are self-contained and algebraic. Eq. (12) rewrites H in the eigenbasis of H0, and Eq. (14) gives E_{n,±} = ±√(E_n² + V² − γ²) by exact diagonalization of each 2×2 block; the result that V=±γ leaves the spectrum unchanged follows directly from this formula, with no fitted constants or imported uniqueness theorem. The sublattice winding number is evaluated at the reference energy ε=±√(V²−γ²), which is the edge-state energy obtained from Eq. (14) and lies in the bulk gap; the invariant is computed directly from h_k in Appendix A, and the edge states are then solved independently from the Schrödinger equation in Appendix B, so the match between w^A=2 and the two edge states per end is a genuine bulk-boundary check rather than an assumed conclusion. The EP dynamics in Eq. (16) is derived from the 2×2 Jordan block, not assumed. Self-citations [36,41,44–48] are background and context and are not load-bearing. Two non-circular caveats exist: the abstract's 'a trivial initial state can always evolve to a stable edge state' is broader than the condition in Eq. (16) that the initial state have nonzero overlap with the non-coalescing direction, and the advertised robustness against local perturbations is not directly tested numerically (the only such check is the global quench in Fig. 3). These are accuracy and evidence issues, not cases where a prediction reduces to its inputs by construction.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The central results rest on the antisymmetric-hopping structure of H0, the equal-sublattice assumption, and the tuned condition V = gamma. No entities are invented. No parameters are fitted to external data; delta, V = gamma, and N are model parameters.

free parameters (3)
  • delta = 0.2 (numerics)
    Alternating hopping dimerization in the SSH ladder (Eq. 20); chosen by hand, controls the topological phase and localization length zeta.
  • V = gamma = 1 (numerics)
    Balanced perturbation strengths; the equality V = gamma is the central condition for the spectral invariance and EP formation, chosen rather than derived.
  • N = 20 (numerics)
    Number of unit cells in the numerical time evolution; finite-size truncation of the infinite-ladder edge-state derivation.
assumptions (5)
  • domain assumption J_ij = -J_ji (antisymmetric hopping between sublattices)
    Eq. (4); ensures the bipartite Hamiltonian can be block-diagonalized into 2x2 blocks with the given structure.
  • domain assumption Equal sublattice sizes N_a = N_b = N
    Used throughout Sec II; required for the pairing of modes into (D_{n,+}, D_{n,-}) 2x2 blocks.
  • domain assumption Balanced perturbation condition V = +/- gamma
    The paper's central tuning; under this condition the spectrum of H equals that of H0 (Sec II), so it is a premise of the main claim rather than a derived fact.
  • domain assumption Absence of non-Hermitian skin effect (imaginary hoppings connect same-index sites)
    Sec II; ensures line-gap topology and the validity of the standard Bloch winding number, stated explicitly in the introduction.
  • standard math Sublattice winding number characterizes the topology (following Refs [15-17])
    Sec III B; used to compute wA and wB for the ladder; taken as the established invariant for systems without chiral or inversion symmetry.

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Pith. "Pith review of Dynamically stable topological edge states in an extended Su-Schrieffer-Heeger ladder with balanced perturbation." pith.science (2026). https://pith.science/paper/6ZTKEMYV

@misc{pith2026250605666,
  author       = {Pith},
  title        = {Pith review of: Dynamically stable topological edge states in an extended Su-Schrieffer-Heeger ladder with balanced perturbation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6ZTKEMYV}},
  note         = {Machine review of arXiv:2506.05666}
}
read the original abstract

The on-site potentials may break the symmetry of a system, resulting in the loss of its original topology protected by the symmetry. In this work, we study the counteracting effect of non-Hermitian terms on real potentials, resulting in dynamically stable topological edge states. We show exactly for a class of systems that the spectrum remains unchanged in the presence of balanced perturbations. As a demonstration, we investigate an extended non-Hermitian Su-Schrieffer-Heeger(SSH) ladder. We find that the bulk-boundary correspondence still holds, and the zero-energy edge states become coalescing states. In comparison to the original SSH chain, such edge states are robust not only against local perturbations but also in the time domain. As a result, a trivial initial state can always evolve to a stable edge state. Our results provide insights for the application of time-domain stable topological quantum devices.

Figures

Figures reproduced from arXiv: 2506.05666 by the authors.

Figure 1
Figure 1. FIG. 1. The Schematic of the extended SSH ladder with imag [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. The spatial distribution of the modulus of the amplitudes of the evolved state (top panels) and the plots of the overlap [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. (a) The spatial distribution of the modulus of the [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

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

  1. Quantum dynamical signatures of non-Hermitian boundary modes

    cond-mat.mes-hall 2025-06 accept novelty 7.0 of 10

    A solvable bosonic SSH chain with sublattice dissipation displays a positive Liouvillian separation gap that dynamically isolates the non-Hermitian boundary mode, yielding detectable density and polarization signatures.

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Works this paper leans on

54 extracted references · 25 canonical work pages · cited by 1 Pith paper

  1. [1]

    K. v. Klitzing, G. Dorda, and M. Pepper, New method for high-accuracy determination of the fine-structure con- stant based on quantized hall resistance, Phys. Rev. Lett. 45, 494 (1980)

    1980

  2. [2]

    D. J. Thouless, M. Kohmoto, M. P. Nightingale, and M. den Nijs, Quantized hall conductance in a two- dimensional periodic potential, Phys. Rev. Lett.49, 405 (1982)

    1982

  3. [3]

    Zak, Berry’s phase for energy bands in solids, Phys

    J. Zak, Berry’s phase for energy bands in solids, Phys. Rev. Lett.62, 2747 (1989)

    1989

  4. [4]

    A. Y. Kitaev, Unpaired majorana fermions in quantum wires, Phys. Usp.44, 131 (2001)

    2001

  5. [5]

    Fu and C

    L. Fu and C. L. Kane, Topological insulators with inver- sion symmetry, Phys. Rev. B76, 045302 (2007)

    2007

  6. [6]

    Nayak, S

    C. Nayak, S. H. Simon, A. Stern, M. Freedman, and S. Das Sarma, Non-abelian anyons and topological quan- tum computation, Rev. Mod. Phys.80, 1083 (2008)

    2008

  7. [7]

    Qi and S.-C

    X.-L. Qi and S.-C. Zhang, Topological insulators and su- perconductors, Rev. Mod. Phys.83, 1057 (2011)

    2011

  8. [8]

    Matsuura, P.-Y

    S. Matsuura, P.-Y. Chang, A. P. Schnyder, and S. Ryu, Protected boundary states in gapless topological phases, New J. Phys.15, 065001 (2013)

    work page 2013

Show all 54 references
  1. [9]

    Chiu and A

    C.-K. Chiu and A. P. Schnyder, Classification of reflection-symmetry-protected topological semimetals 8 and nodal superconductors, Phys. Rev. B90, 205136 (2014)

    2014

  2. [10]

    S. D. Sarma, M. Freedman, and C. Nayak, Majorana zero modes and topological quantum computation, npj Quantum Information1, 1 (2015)

    2015

  3. [11]

    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

  4. [12]

    J. K. Asb´ oth, L. Oroszl´ any, and A. P´ alyi,A short course on topological insulators(Springer, 2016)

    2016

  5. [13]

    Kobayashi, S

    S. Kobayashi, S. Sumita, Y. Yanase, and M. Sato, Symmetry-protected line nodes and majorana flat bands in nodal crystalline superconductors, Phys. Rev. B97, 180504 (2018)

    2018

  6. [14]

    L. Xie, L. Jin, and Z. Song, Antihelical edge states in two-dimensional photonic topological metals, Sci. Bull. 68, 255 (2023)

    2023

  7. [15]

    J.-W. Rhim, J. Behrends, and J. H. Bardarson, Bulk- boundary correspondence from the intercellular zak phase, Phys. Rev. B95, 035421 (2017)

    2017

  8. [16]

    Guzm´ an, D

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

    2022

  9. [17]

    Verma and T

    S. Verma and T. K. Ghosh, Bulk-boundary correspon- dence in extended trimer su-schrieffer-heeger model, Phys. Rev. B110, 125424 (2024)

    2024

  10. [18]

    D. V. Else, P. Fendley, J. Kemp, and C. Nayak, Prether- mal strong zero modes and topological qubits, Phys. Rev. X7, 041062 (2017)

    2017

  11. [19]

    M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, and A. Sza- meit, Photonic floquet topological insulators, Nature 496, 196 (2013)

    2013

  12. [20]

    Lohse, C

    M. Lohse, C. Schweizer, H. M. Price, O. Zilberberg, and I. Bloch, Exploring 4d quantum hall physics with a 2d topological charge pump, Nature553, 55 (2018)

    2018

  13. [21]

    Sun, C.-R

    W. Sun, C.-R. Yi, B.-Z. Wang, W.-W. Zhang, B. C. Sanders, X.-T. Xu, Z.-Y. Wang, J. Schmiedmayer, Y. Deng, X.-J. Liu, S. Chen, and J.-W. Pan, Uncover topology by quantum quench dynamics, Phys. Rev. Lett. 121, 250403 (2018)

    2018

  14. [22]

    Zhang, Y.-Q

    D.-W. Zhang, Y.-Q. Zhu, Y. Zhao, H. Yan, and S.-L. Zhu, Topological quantum matter with cold atoms, Adv. Phys.67, 253 (2018)

    2018

  15. [23]

    J. Li, A. K. Harter, J. Liu, L. de Melo, Y. N. Joglekar, and L. Luo, Observation of parity-time symmetry breaking transitions in a dissipative Floquet system of ultracold atoms, Nat. Commun.10, 855 (2019)

    2019

  16. [24]

    Barbarino, J

    S. Barbarino, J. Yu, P. Zoller, and J. C. Budich, Prepar- ing atomic topological quantum matter by adiabatic nonunitary dynamics, Phys. Rev. Lett.124, 010401 (2020)

    2020

  17. [25]

    M. S. Rudner and N. H. Lindner, Band structure engi- neering and non-equilibrium dynamics in floquet topo- logical insulators, Nat. Rev. Phys.2, 229 (2020)

    2020

  18. [26]

    Zhang, L

    L. Zhang, L. Zhang, and X.-J. Liu, Unified theory to char- acterize floquet topological phases by quench dynamics, Phys. Rev. Lett.125, 183001 (2020)

    2020

  19. [27]

    Citro and M

    R. Citro and M. Aidelsburger, Thouless pumping and topology, Nat. Rev. Phys.5, 87 (2023)

    2023

  20. [28]

    Bin, L.-L

    Q. Bin, L.-L. Wan, F. Nori, Y. Wu, and X.-Y. L¨ u, Out-of- time-order correlation as a witness for topological phase transitions, Phys. Rev. B107, L020202 (2023)

    2023

  21. [29]

    T. L. M. Lane, M. Horv´ ath, and K. Patrick, Extended edge modes and disorder preservation of a symmetry- protected topological phase out of equilibrium, Phys. Rev. B110, 165139 (2024)

    2024

  22. [30]

    Jin, Topological phases and edge states in a non- hermitian trimerized optical lattice, Phys

    L. Jin, Topological phases and edge states in a non- hermitian trimerized optical lattice, Phys. Rev. A96, 032103 (2017)

    2017

  23. [31]

    Takata and M

    K. Takata and M. Notomi, Photonic topological insulat- ing phase induced solely by gain and loss, Phys. Rev. Lett.121, 213902 (2018)

    2018

  24. [32]

    Harari, M

    G. Harari, M. A. Bandres, Y. Lumer, M. C. Rechtsman, Y. D. Chong, M. Khajavikhan, D. N. Christodoulides, and M. Segev, Topological insulator laser: theory, Science 359, 10.1126/science.aar4003 (2018)

    2018 doi

  25. [33]

    M. A. Bandres, S. Wittek, G. Harari, M. Parto, J. Ren, M. Segev, D. N. Christodoulides, and M. Khajavikhan, Topological insulator laser: Experiments, Science359, 10.1126/science.aar4005 (2018)

    2018 doi

  26. [34]

    S. Yao, F. Song, and Z. Wang, Non-hermitian chern bands, Phys. Rev. Lett.121, 136802 (2018)

    2018

  27. [35]

    Yao and Z

    S. Yao and Z. Wang, Edge states and topological in- variants of non-hermitian systems, Phys. Rev. Lett.121, 086803 (2018)

    2018

  28. [36]

    Jin and Z

    L. Jin and Z. Song, Bulk-boundary correspondence in a non-hermitian system in one dimension with chiral inver- sion symmetry, Phys. Rev. B99, 081103 (2019)

    2019

  29. [37]

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

    2019

  30. [38]

    Luo and C

    X.-W. Luo and C. Zhang, Higher-order topological corner states induced by gain and loss, Phys. Rev. Lett.123, 073601 (2019)

    2019

  31. [39]

    Zhang and J

    X. Zhang and J. Gong, Non-hermitian floquet topological phases: Exceptional points, coalescent edge modes, and the skin effect, Phys. Rev. B101, 045415 (2020)

    2020

  32. [40]

    Zhou and Q

    L. Zhou and Q. Du, Non-hermitian topological phases and dynamical quantum phase transitions: A generic connection, New J. Phys.23, 063041 (2021)

    2021

  33. [41]

    H. C. Wu, L. Jin, and Z. Song, Topology of an anti- parity-time symmetric non-hermitian su-schrieffer-heeger model, Phys. Rev. B103, 235110 (2021)

    2021

  34. [42]

    Roccati, M

    F. Roccati, M. Bello, Z. Gong, M. Ueda, F. Ciccarello, A. Chenu, and A. Carollo, Hermitian and non-hermitian topology from photon-mediated interactions, Nat. Com- mun.15, 2400 (2024)

    2024

  35. [43]

    Huang, S

    L. Huang, S. Huang, C. Shen, S. Yves, A. S. Pilipchuk, X. Ni, S. Kim, Y. K. Chiang, D. A. Powell, J. Zhu,et al., Acoustic resonances in non-hermitian open systems, Nat. Rev. Phys.6, 11 (2024)

    2024

  36. [44]

    K. L. Zhang, P. Wang, and Z. Song, Exceptional-point- induced lasing dynamics in a non-hermitian su-schrieffer- heeger model, Phys. Rev. A99, 042111 (2019)

    2019

  37. [45]

    K. L. Zhang, L. Jin, and Z. Song, Helical resonant trans- port and purified amplification at an exceptional point, Phys. Rev. B100, 144301 (2019)

    2019

  38. [46]

    C. Wang, W. R. Sweeney, A. D. Stone, and L. Yang, Co- herent perfect absorption at an exceptional point, Science 373, 1261 (2021)

    2021

  39. [47]

    P. Wang, K. L. Zhang, and Z. Song, Transition from degeneracy to coalescence: Theorem and applications, Phys. Rev. B104, 245406 (2021)

    2021

  40. [48]

    Y. Shi, K. Zhang, and Z. Song, Exceptional spectrum and dynamic magnetization, J. Phys.:Condens. Matter 34, 485401 (2022)

    2022

  41. [49]

    Longhi, Self-healing of non-hermitian topological skin 9 modes, Phys

    S. Longhi, Self-healing of non-hermitian topological skin 9 modes, Phys. Rev. Lett.128, 157601 (2022)

    2022

  42. [50]

    W.-T. Xue, F. Song, Y.-M. Hu, and Z. Wang, Non-bloch edge dynamics of non-hermitian lattices, arXiv preprint arXiv:2503.13671 (2025)

    2025 arXiv

  43. [51]

    Y. Miao, Y. Zhao, Y. Wang, J. Qiao, X. Zhao, and X. Yi, Non-abelian gauge enhances self-healing for non-hermitian su–schrieffer–heeger chain, arXiv preprint arXiv:2503.23978 (2025)

    2025

  44. [52]

    Mostafazadeh, Pseudo-hermiticity versus pt- symmetry iii: Equivalence of pseudo-hermiticity and the presence of antilinear symmetries, J

    A. Mostafazadeh, Pseudo-hermiticity versus pt- symmetry iii: Equivalence of pseudo-hermiticity and the presence of antilinear symmetries, J. Math. Phys.43, 3944 (2002)

    2002

  45. [53]

    W. P. Su, J. R. Schrieffer, and A. J. Heeger, Solitons in polyacetylene, Phys. Rev. Lett.42, 1698 (1979)

    1979

  46. [54]

    M. J. Rice and E. J. Mele, Elementary excitations of a linearly conjugated diatomic polymer, Phys. Rev. Lett. 49, 1455 (1982)

    1982

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