arxiv: 2601.13619 · v3 · submitted 2026-01-20 · ❄️ cond-mat.dis-nn · cond-mat.mes-hall· quant-ph

Recognition: no theorem link

Recent progress on disorder-induced topological phases

Dan-Wei Zhang , Ling-Zhi Tang

Authors on Pith no claims yet

Pith reviewed 2026-05-16 13:05 UTC · model grok-4.3

classification ❄️ cond-mat.dis-nn cond-mat.mes-hallquant-ph

keywords disorder-induced topologytopological Anderson insulatorstopological phasesdisordered systemsquasiperiodic systemsnon-Hermitian systemsmany-body topology

0 comments

The pith

Disorder can induce topological phases from a clean-limit trivial phase.

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

The paper reviews how random disorders counterintuitively create topological states in systems that lack them when clean. It covers topological Anderson insulators, their characterizations, and extensions to quasiperiodic, non-Hermitian, dynamical, and many-body systems. A sympathetic reader would care because this mechanism suggests disorder can be harnessed to produce robust topological behavior rather than merely destroying it. The review compiles theoretical models and experimental realizations across condensed-matter and artificial platforms. This points to new routes for engineering topological matter without requiring perfect cleanliness.

Core claim

Disorders can induce topological phases such as topological Anderson insulators from a topologically trivial phase in the clean limit. These induced states remain robust against certain disorders. The review summarizes their topological characterizations and experimental realizations, then extends the discussion to quasiperiodic and non-Hermitian systems with unique localization phenomena, and to dynamical and many-body systems including topological Anderson-Thouless pumps, disordered correlated topological insulators, and average-symmetry protected topological orders.

What carries the argument

Topological Anderson insulators (TAIs), topological states induced by random disorders in otherwise trivial clean systems.

Load-bearing premise

The cited theoretical models and experimental realizations correctly demonstrate disorder-induced topological characters without major overlooked competing effects or mischaracterizations.

What would settle it

A controlled experiment or numerical simulation in which increasing disorder strength fails to produce the predicted topological invariants or edge states in a system expected to form a topological Anderson insulator.

Figures

Figures reproduced from arXiv: 2601.13619 by Dan-Wei Zhang, Ling-Zhi Tang.

**Figure 2.** Figure 2: FIG. 2. Observation of the TAI in disordered atomic wires. [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3. Photonic TAIs. (a) Schematic of the 2D waveguide [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4. (Color online) (a) Real-space winding number [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗

**Figure 5.** Figure 5: FIG. 5. (Color online) (a) Global phase diagram in the [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗

**Figure 6.** Figure 6: FIG. 6. (Color online) (a) Photograph of the programmable superconducting simulator. (b) Schematic of the gSSH model [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗

**Figure 7.** Figure 7: FIG. 7. (Color online) (a) Sketch of the non-Hermitian disor [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗

**Figure 8.** Figure 8: FIG. 8. (Color online) (a) Sketch of the generalized SSH [PITH_FULL_IMAGE:figures/full_fig_p013_8.png] view at source ↗

**Figure 10.** Figure 10: FIG. 10. (Color online) (a) Illustration of the operation se [PITH_FULL_IMAGE:figures/full_fig_p014_10.png] view at source ↗

**Figure 9.** Figure 9: FIG. 9. (Color online) (a) Schematic of the non-Hermitian [PITH_FULL_IMAGE:figures/full_fig_p014_9.png] view at source ↗

**Figure 11.** Figure 11: FIG. 11. (Color online) Point-gap winding number [PITH_FULL_IMAGE:figures/full_fig_p016_11.png] view at source ↗

**Figure 1.** Figure 1: FIG. 1. Schematic of extrinsic and intrinsic topological pumps induced by (a) on-site and (b) hopping quasiperiodic disorders. Pump olor online) Topological pumps driven by (a) onsite disorder V and (b) hopping disorder WPump loops in [PITH_FULL_IMAGE:figures/full_fig_p017_1.png] view at source ↗

**Figure 2.** Figure 2: FIG. 2. (a) Schematic of TATP in the e to gap closure (Emin gin = 0) [PITH_FULL_IMAGE:figures/full_fig_p017_2.png] view at source ↗

**Figure 13.** Figure 13: FIG. 13. (Color online) (a) Optical micrograph of the 43- [PITH_FULL_IMAGE:figures/full_fig_p019_13.png] view at source ↗

**Figure 1.** Figure 1: FIG. 1. (a) Schematic of proposed model. (b) Phase diagram of Hilti(1) thW U lThd ilbl FIG. 14. (Color online) (a) Schematic of the model Hamilto [PITH_FULL_IMAGE:figures/full_fig_p020_1.png] view at source ↗

**Figure 15.** Figure 15: FIG. 15. (a) Schematics of a dimerized Rydberg atom chain [PITH_FULL_IMAGE:figures/full_fig_p021_15.png] view at source ↗

**Figure 16.** Figure 16: FIG. 16. (a) Schematics of a 1D dimerized Rydberg atom [PITH_FULL_IMAGE:figures/full_fig_p022_16.png] view at source ↗

read the original abstract

Topological states of matter in disordered systems without translation symmetry have attracted great interest in recent years. These states with topological characters are not only robust against certain disorders, but also can be counterintuitively induced by disorders from a topologically trivial phase in the clean limit. In this review, we summarize the current theoretical and experimental progress on disorder-induced topological phases in both condensed-matter and artificial systems. We first introduce the topological Anderson insulators (TAIs) induced by random disorders and their topological characterizations and experimental realizations. We then discuss various extensions of TAIs with unique localization phenomena in quasiperiodic and non-Hermitian systems. We also review the theoretical and experimental studies on the disorder-induced topology in dynamical and many-body systems, including topological Anderson-Thouless pumps, disordered correlated topological insulators and average-symmetry protected topological orders acting as interacting TAI phases. Finally, we conclude the review by highlighting potential directions for future explorations.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

This is a review that organizes existing work on disorder-induced topological phases without adding new results or frameworks.

read the letter

The main thing to know is that this paper is a review summarizing literature on how disorder can induce topological character in systems that are trivial when clean. It covers topological Anderson insulators from random disorder, then extensions into quasiperiodic, non-Hermitian, dynamical, and interacting cases, including some experimental mentions in artificial systems. The structure is straightforward and the abstract presents the central counterintuitive point consistently with the cited models. That organization is the useful part for someone who wants a quick map of the subfield. The authors stick to established results rather than claiming fresh derivations or data, so the value rests on how accurately they represent the prior papers. No internal contradictions show up in the summary itself, and the citation pattern looks external rather than self-referential. A minor limitation is that any review can lag behind the very latest preprints or underplay open questions in the underlying simulations, such as finite-size effects or competing localization mechanisms. Readers will still need to go back to the original works for details. This is aimed at condensed-matter physicists already familiar with topology who need an entry point to the disorder angle. It does not break new ground, but a current snapshot of an active area can still be worth referee time for a review journal. I would send it out for peer review rather than desk reject.

Referee Report

0 major / 2 minor

Summary. The manuscript is a review summarizing theoretical and experimental progress on disorder-induced topological phases. It begins with topological Anderson insulators (TAIs) induced by random disorders, including their topological characterizations and experimental realizations, then covers extensions to quasiperiodic and non-Hermitian systems, and concludes with disorder-induced topology in dynamical and many-body systems such as topological Anderson-Thouless pumps, disordered correlated topological insulators, and average-symmetry protected topological orders.

Significance. If the cited literature is represented accurately, the review is significant as a consolidation of work showing that disorder can induce topological character from a clean-limit trivial phase. It provides a broad, accessible overview across condensed-matter and artificial systems, which is useful for researchers entering or working in this area. The manuscript draws directly from external references without internal derivations or new claims.

minor comments (2)

[Abstract] The abstract could more explicitly list the distinct classes of systems (quasiperiodic, non-Hermitian, dynamical, interacting) covered after the TAI introduction to improve reader orientation.
Section headings and subheadings would benefit from consistent numbering or clearer hierarchical formatting to help readers navigate the progression from TAIs to extensions.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of our manuscript as a useful consolidation of progress on disorder-induced topological phases. We appreciate the recommendation for minor revision and the recognition of its broad overview across condensed-matter and artificial systems. No major comments were provided in the report, so we have no specific points to address at this time. We remain ready to incorporate any minor editorial suggestions or additional feedback from the editor.

Circularity Check

0 steps flagged

Review paper summarizes external literature; no internal derivation chain present

full rationale

This is a review article that compiles and summarizes results from cited external literature on topological Anderson insulators and related phenomena in disordered, quasiperiodic, non-Hermitian, dynamical, and interacting systems. The abstract and structure present no original derivations, equations, or first-principles predictions that could reduce to self-referential inputs, fitted parameters renamed as predictions, or self-citation chains. All load-bearing claims are explicitly attributed to prior independent works, satisfying the guideline that externally cited results (when not overlapping in a load-bearing unverified way) constitute real evidence rather than circularity. No self-definitional steps, ansatz smuggling, or renaming of known results occur within the manuscript itself.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

As a review paper the central content rests on the body of cited literature rather than new postulates; no free parameters, axioms, or invented entities are introduced by this work itself.

pith-pipeline@v0.9.0 · 5456 in / 871 out tokens · 23911 ms · 2026-05-16T13:05:00.440801+00:00 · methodology

discussion (0)

Forward citations

Cited by 1 Pith paper

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

Finite-temperature topological transitions in the presence of quenched uncorrelated disorder
cond-mat.dis-nn 2026-01 unverdicted novelty 6.0

Weak uncorrelated quenched disorder drives the topological transition of the 3D Z2 gauge model into a new universality class, consistent with the Harris criterion.

Reference graph

Works this paper leans on

300 extracted references · 300 canonical work pages · cited by 1 Pith paper · 1 internal anchor

[1]

The valueγ= 1 corresponds to a topological phase, whileγ= 0 for a trivial phase

Phase diagram The topological nature of this 1D interacting system can be captured by a many-body Berry phase quantized in units ofπunder twisted PBCs [273]: γ= 1 π I dθ⟨Ψ g(θ)|i∂ θ |Ψg(θ)⟩mod 2,(27) where|Ψ g(θ)⟩denotes the half-filled many-body ground state in the presence of a twist angleθ. The valueγ= 1 corresponds to a topological phase, whileγ= 0 fo...

work page 2021
[2]

Two dimensions The disorder effect on interacting topological insula- tors of 2D fermions has been investigated in Ref. [283]. Although the absence of disorder-induced TAIs, it was found that the topological phases are stable against dis- orders even when interactions are included. In the spin- ful Harper-Hofstadter-Hatsugai model on a 2D square lattice [...

work page
[3]

[210], the authors studied topological phases in a 1D amorphous Rydberg atom chain with random atom configurations

Proposal with Rydberg atom arrays In Ref. [210], the authors studied topological phases in a 1D amorphous Rydberg atom chain with random atom configurations. In the single-particle level, the topologi- cal amorphous insulators induced by the structural dis- order was found. Moreover, a symmetry-protected topo- logical phase of interacting bosons in this d...

work page
[4]

relative to the magnetic field, the hopping within each sublat- tice is suppressed and the chiral symmetry is achieved. The structural disorder is introduced by displacing atoms from their ordered positions viaz 2i−1 →i−1 +δz i and z2i →i−1 +R z +δz i, with eachδz i being uniformly drawn from [−W/2, W/2] and disorder strengthW. When there is only one exci...

work page
[5]

Similar to the proposal in Ref

Experimental realization In a recent experiment [290], the disorder-induced in- teracting average symmetry protected topological phase has been realized in a Rydberg atom array. Similar to the proposal in Ref. [210], the Rydberg atom array is dimer- ized with two sub-chains (denoted byαandβ), and the structural disorder is introduced by randomly displacin...

work page
[6]

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

work page 2010
[7]

Qi and S.-C

X.-L. Qi and S.-C. Zhang, Topological insulators and 25 superconductors, Rev. Mod. Phys.83, 1057 (2011)

work page 2011
[8]

Bansil, H

A. Bansil, H. Lin, and T. Das, Colloquium: Topological band theory, Rev. Mod. Phys.88, 021004 (2016)

work page 2016
[9]

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)

work page 2016
[10]

N. P. Armitage, E. J. Mele, and A. Vishwanath, Weyl and dirac semimetals in three-dimensional solids, Rev. Mod. Phys.90, 015001 (2018)

work page 2018
[11]

Y. B. Yang, J. H. Wang, K. Li, and Y. Xu, Higher-order topological phases in crystalline and non-crystalline sys- tems: a review, J. Phys.: Condens. Matter36, 283002 (2024)

work page 2024
[12]

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

work page 1980
[13]

D. C. Tsui, H. L. Stormer, and A. C. Gossard, Two- dimensional magnetotransport in the extreme quantum limit, Phys. Rev. Lett.48, 1559 (1982)

work page 1982
[14]

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)

work page 1982
[15]

F. D. M. Haldane, Model for a quantum hall effect with- out landau levels: Condensed-matter realization of the ”parity anomaly”, Phys. Rev. Lett.61, 2015 (1988)

work page 2015
[16]

B. A. Bernevig, T. L. Hughes, and S.-C. Zhang, Quan- tum spin hall effect and topological phase transition in hgte quantum wells, Science314, 1757 (2006)

work page 2006
[17]

P. W. Anderson, Absence of diffusion in certain random lattices, Phys. Rev.109, 1492 (1958)

work page 1958
[18]

Evers and A

F. Evers and A. D. Mirlin, Anderson transitions, Rev. Mod. Phys.80, 1355 (2008)

work page 2008
[19]

J. Li, R. L. Chu, J. K. Jain, and S. Q. Shen, Topolog- ical anderson insulator, Phys. Rev. Lett.102, 136806 (2009)

work page 2009
[20]

Goldman, J

N. Goldman, J. C. Budich, and P. Zoller, Topological quantum matter with ultracold gases in optical lattices, Nat. Phys.12, 639 (2016)

work page 2016
[21]

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

work page 2018
[22]

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

work page 2019
[23]

L. Lu, J. D. Joannopoulos, and M. Soljaˇ ci´ c, Topological photonics, Nat. Photonics8, 821 (2014)

work page 2014
[24]

Ozawa, H

T. Ozawa, H. M. Price, A. Amo, N. Goldman, M. Hafezi, L. Lu, M. C. Rechtsman, D. Schuster, J. Si- mon, O. Zilberberg, and I. Carusotto, Topological pho- tonics, Rev. Mod. Phys.91, 015006 (2019)

work page 2019
[25]

F. D. M. Haldane and S. Raghu, Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry, Phys. Rev. Lett.100, 013904 (2008)

work page 2008
[26]

M. D. Schroer, M. H. Kolodrubetz, W. F. Kindel, M. Sandberg, J. Gao, M. R. Vissers, D. P. Pappas, A. Polkovnikov, and K. W. Lehnert, Measuring a topo- logical transition in an artificial spin-1/2 system, Phys. Rev. Lett.113, 050402 (2014)

work page 2014
[27]

Roushan, C

P. Roushan, C. Neill, Y. Chen, M. Kolodrubetz, C. Quintana, N. Leung, M. Fang, R. Barends, B. Camp- bell, Z. Chen, B. Chiaro, A. Dunsworth, E. Jeffrey, J. Kelly, A. Megrant, J. Mutus, P. J. J. O’Malley, D. Sank, A. Vainsencher, J. Wenner, T. White, A. Polkovnikov, A. N. Cleland, and J. M. Martinis, Ob- servation of topological transitions in interacting q...

work page 2014
[28]

X. Tan, D. W. Zhang, Q. Liu, G. Xue, H. F. Yu, Y. Q. Zhu, H. Yan, S. L. Zhu, and Y. Yu, Topological Maxwell Metal Bands in a Superconducting Qutrit, Phys. Rev. Lett.120, 130503 (2018)

work page 2018
[29]

Tan, D.-W

X. Tan, D.-W. Zhang, Z. Yang, J. Chu, Y.-Q. Zhu, D. Li, X. Yang, S. Song, Z. Han, Z. Li, Y. Dong, H.-F. Yu, H. Yan, S.-L. Zhu, and Y. Yu, Experimen- tal measurement of the quantum metric tensor and re- lated topological phase transition with a superconduct- ing qubit, Phys. Rev. Lett.122, 210401 (2019)

work page 2019
[30]

Tan, D.-W

X. Tan, D.-W. Zhang, W. Zheng, X. Yang, S. Song, Z. Han, Y. Dong, Z. Wang, D. Lan, H. Yan, S.-L. Zhu, and Y. Yu, Experimental observation of tensor monopoles with a superconducting qudit, Phys. Rev. Lett.126, 017702 (2021)

work page 2021
[31]

J. Deng, H. Dong, C. Zhang, Y. Wu, J. Yuan, X. Zhu, F. Jin, H. Li, Z. Wang, H. Cai, C. Song, H. Wang, J. Q. You, and D.-W. Wang, Observing the quantum topology of light, Science378, 966 (2022)

work page 2022
[32]

Ashida, Z

Y. Ashida, Z. Gong, and M. Ueda, Non-hermitian physics, Adv. Phys.69, 249 (2020)

work page 2020
[33]

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

work page 2021
[34]

Ghatak and T

A. Ghatak and T. Das, New topological invariants in non-hermitian systems, J. Phys.: Condens. Matter31, 263001 (2019)

work page 2019
[35]

Okuma and M

N. Okuma and M. Sato, Non-hermitian topological phe- nomena: A review, Annual Review of Condensed Mat- ter Physics14, 83 (2023)

work page 2023
[36]

Banerjee, R

A. Banerjee, R. Sarkar, S. Dey, and A. Narayan, Non- hermitian topological phases: principles and prospects, J. Phys.: Condens. Matter35, 333001 (2023)

work page 2023
[37]

H.-Z. Li, Z. Jianxin, and X.-J. Yu, Measurement- Induced Entanglement Phase Transition in Free Fermion Systems, J. Phys.: Condens. Matter37, 273002 (2025)

work page 2025
[38]

C. M. Bender and S. Boettcher, Real spectra in non- hermitian hamiltonians having pt symmetry, Phys. Rev. Lett.80, 5243 (1998)

work page 1998
[39]

L. Feng, R. El-Ganainy, and L. Ge, Non-hermitian pho- tonics based on parity–time symmetry, Nat. Photonics 11, 752 (2017)

work page 2017
[40]

El-Ganainy, K

R. El-Ganainy, K. G. Makris, M. Khajavikhan, Z. H. Musslimani, S. Rotter, and D. N. Christodoulides, Non- hermitian physics and pt symmetry, Nat. Phys.14, 11 (2018)

work page 2018
[41]

Miri and A

M.-A. Miri and A. Al` u, Exceptional points in optics and photonics, Science363, 6422 (2019)

work page 2019
[42]

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

work page 2016
[43]

Yao and Z

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

work page 2018
[44]

F. Song, S. Yao, and Z. Wang, Non-hermitian topologi- cal invariants in real space, Phys. Rev. Lett.123, 246801 (2019)

work page 2019
[45]

Z. Gong, Y. Ashida, K. Kawabata, K. Takasan, S. Hi- gashikawa, and M. Ueda, Topological phases of non- 26 hermitian systems, Phys. Rev. X8, 031079 (2018)

work page 2018
[46]

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

work page 2018
[47]

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)

work page 2017
[48]

Jin and Z

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

work page 2019
[49]

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)

work page 2020
[50]

Zhang, Y.-L

D.-W. Zhang, Y.-L. Chen, G.-Q. Zhang, L.-J. Lang, Z. Li, and S.-L. Zhu, Skin superfluid, topological mott insulators, and asymmetric dynamics in an interacting non-hermitian aubry-andr´ e-harper model, Phys. Rev. B 101, 235150 (2020)

work page 2020
[51]

Hatano and D

N. Hatano and D. R. Nelson, Localization transitions in non-hermitian quantum mechanics, Phys. Rev. Lett. 77, 570 (1996)

work page 1996
[52]

Hatano and D

N. Hatano and D. R. Nelson, Vortex pinning and non- hermitian quantum mechanics, Phys. Rev. B56, 8651 (1997)

work page 1997
[53]

Longhi, Topological phase transition in non- hermitian quasicrystals, Phys

S. Longhi, Topological phase transition in non- hermitian quasicrystals, Phys. Rev. Lett.122, 237601 (2019)

work page 2019
[54]

Jiang, L.-J

H. Jiang, L.-J. Lang, C. Yang, S.-L. Zhu, and S. Chen, Interplay of non-hermitian skin effects and anderson lo- calization in nonreciprocal quasiperiodic lattices, Phys. Rev. B100, 054301 (2019)

work page 2019
[55]

Hamazaki, K

R. Hamazaki, K. Kawabata, and M. Ueda, Non- hermitian many-body localization, Phys. Rev. Lett. 123, 090603 (2019)

work page 2019
[56]

L.-J. Zhai, S. Yin, and G.-Y. Huang, Many-body local- ization in a non-hermitian quasiperiodic system, Phys. Rev. B102, 064206 (2020)

work page 2020
[57]

Tang, G.-Q

L.-Z. Tang, G.-Q. Zhang, L.-F. Zhang, and D.-W. Zhang, Localization and topological transitions in non- hermitian quasiperiodic lattices, Phys. Rev. A103, 033325 (2021)

work page 2021
[58]

Zhang, L.-Z

L.-F. Zhang, L.-Z. Tang, Z.-H. Huang, G.-Q. Zhang, W. Huang, and D.-W. Zhang, Machine learning topo- logical invariants of non-hermitian systems, Phys. Rev. A103, 012419 (2021)

work page 2021
[59]

Zhai, G.-Y

L.-J. Zhai, G.-Y. Huang, and S. Yin, Nonequilibrium dynamics of the localization-delocalization transition in the non-hermitian aubry-andr´ e model, Phys. Rev. B 106, 014204 (2022)

work page 2022
[60]

Dong, E.-W

J.-L. Dong, E.-W. Liang, S.-Y. Liu, G.-Q. Zhang, L.-Z. Tang, and D.-W. Zhang, Critical properties in the non- hermitian aubry-andr´ e-stark model, Phys. Rev. B111, 174209 (2025)

work page 2025
[61]

J.-F. Ren, J. Li, H.-T. Ding, and D.-W. Zhang, Iden- tifying non-hermitian critical points with the quantum metric, Phys. Rev. A110, 052203 (2024)

work page 2024
[62]

L. Wang, Z. Wang, and S. Chen, Non-hermitian butter- fly spectra in a family of quasiperiodic lattices, Phys. Rev. B110, L060201 (2024)

work page 2024
[63]

Li and Z

S.-Z. Li and Z. Li, Ring structure in the complex plane: A fingerprint of a non-hermitian mobility edge, Phys. Rev. B110, L041102 (2024)

work page 2024
[64]

Chen, G.-Q

R.-J. Chen, G.-Q. Zhang, Z. Li, and D.-W. Zhang, Mo- bility rings in a non-hermitian non-abelian quasiperiodic lattice, Phys. Rev. A112, 013320 (2025)

work page 2025
[65]

D. J. Thouless, Quantization of particle transport, Phys. Rev. B27, 6083 (1983)

work page 1983
[66]

Mondragon-Shem, T

I. Mondragon-Shem, T. L. Hughes, J. Song, and E. Pro- dan, Topological criticality in the chiral-symmetric AIII class at strong disorder, Phys. Rev. Lett.113, 046802 (2014)

work page 2014
[67]

Song and E

J. Song and E. Prodan, Aiii and bdi topological systems at strong disorder, Phys. Rev. B89, 224203 (2014)

work page 2014
[68]

Altland, D

A. Altland, D. Bagrets, L. Fritz, A. Kamenev, and H. Schmiedt, Quantum criticality of quasi-one- dimensional topological anderson insulators, Phys. Rev. Lett.112, 206602 (2014)

work page 2014
[69]

Altland, D

A. Altland, D. Bagrets, and A. Kamenev, Topology ver- sus Anderson localization: Nonperturbative solutions in one dimension, Phys. Rev. B91, 085429 (2015)

work page 2015
[70]

H. C. Hsu and T. W. Chen, Topological Anderson in- sulating phases in the long-range Su-Schrieffer-Heeger model, Phys. Rev. B102, 205425 (2020)

work page 2020
[71]

Zhang and A

H. Zhang and A. Kamenev, Anatomy of topological An- derson transitions, Phys. Rev. B108, 224201 (2023)

work page 2023
[72]

Velury, B

S. Velury, B. Bradlyn, and T. L. Hughes, Topological crystalline phases in a disordered inversion-symmetric chain, Phys. Rev. B103, 024205 (2021)

work page 2021
[73]

Bellissard, A

J. Bellissard, A. van Elst, and H. Schulz-Baldes, The noncommutative geometry of the quantum hall effect, J. Math. Phys.35, 5373 (1994)

work page 1994
[74]

Collet, M

M. Collet, M. Ouisse, M. Ruzzene, and M. Ichchou, Flo- quet–bloch decomposition for the computation of dis- persion of two-dimensional periodic, damped mechani- cal systems, Int. J. Solids Struct.48, 2837 (2011)

work page 2011
[75]

Huang and F

H. Huang and F. Liu, Theory of spin Bott index for quantum spin Hall states in nonperiodic systems, Phys. Rev. B98, 125130 (2018)

work page 2018
[76]

Huang and F

H. Huang and F. Liu, Quantum Spin Hall Effect and Spin Bott Index in a Quasicrystal Lattice, Phys. Rev. Lett.121, 126401 (2018)

work page 2018
[77]

B. Kang, K. Shiozaki, and G. Y. Cho, Many-body order parameters for multipoles in solids, Phys. Rev. B100, 245134 (2019)

work page 2019
[78]

W. A. Wheeler, L. K. Wagner, and T. L. Hughes, Many- body electric multipole operators in extended systems, Phys. Rev. B100, 245135 (2019)

work page 2019
[79]

Roy, Antiunitary symmetry protected higher-order topological phases, Phys

B. Roy, Antiunitary symmetry protected higher-order topological phases, Phys. Rev. Research1, 032048 (2019)

work page 2019
[80]

Cardano, A

F. Cardano, A. D’Errico, A. Dauphin, M. Maffei, B. Pic- cirillo, C. de Lisio, G. De Filippis, V. Cataudella, E. Santamato, L. Marrucci, M. Lewenstein, and P. Massignan, Detection of zak phases and topological invariants in a chiral quantum walk of twisted photons, Nat. Commun.8, 15516 (2017)

work page 2017

Showing first 80 references.