Exceptional topology of non-Hermitian systems

Bergholtz, Emil J.; Budich, Jan Carl; Kunst, Flore K.

doi:10.1103/revmodphys.93.015005

Cited by 1,711

The DOI matches its Crossref record; 28 of the 28 references it cites were found in a registry or an index.

Exceptional topology of non-Hermitian systems

Bergholtz, Emil J., Budich, Jan Carl, Kunst, Flore K.·2021·Reviews of Modern Physics

DOI 10.1103/revmodphys.93.015005

Open this paper in CoChat — free account

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

Integrity signals

Registry

Crossref · 10.1103/revmodphys.93.015005

Cites

28 of 28 references verified0 citation errors · 0 not checkable

Statistics

Claims the paper makes

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

Under appropriate approximation, a dissipative open quantum system can be mapped to a non-Hermitian Hamiltonian.
“Under appropriate approximation, the dissipative open quantum system can be mapped to a non-Hermitian Hamiltonian2.”
From Non-Hermitian interacting quantum walks of correlated photons (2025) · cites this paper as [2]

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

The self-check needs the paper’s full text.

Topological insulators and superconductors
Qi, X.-L., & Zhang, S.-C. (2011) · Reviews of Modern Physics · doi:10.1103/revmodphys.83.1057 · Cited by 14,394
On the generators of quantum dynamical semigroups
Lindblad, G. (1976) · Communications in Mathematical Physics · doi:10.1007/bf01608499 · Cited by 7,548 · cited 4×
“In such situations, the relevant equation of motion for the reduced density matrix ρ of the open system is the Lindblad master equation (Lindblad, 1976)”
Influential
The Theory of Open Quantum Systems
Breuer, H.-P., & Petruccione, F. (2007) · doi:10.1093/acprof:oso/9780199213900.001.0001 · Cited by 5,938
Weyl and Dirac semimetals in three-dimensional solids
Armitage, N. P., Mele, E. J., & Vishwanath, A. (2018) · Reviews of Modern Physics · doi:10.1103/revmodphys.90.015001 · Cited by 4,528 · cited 8×
“…difference from their Hermitian counterpart is that NH Fermi arcs are a bulk phenomenon (similar in this regard to standard Fermi surfaces), while the surface Fermi arcs in 3D Weyl semimetals connect the projection of the Weyl points to a given surface (Armitage, Mele, and Vishwanath, 2018).”
Influential
Topological photonics
Ozawa, T., Price, H. M., Amo, A., Goldman, N., Hafezi, M., Lu, L., Rechtsman, M. C., Schuster, D., Simon, J., Zilberberg, O., et al. (2019) · Reviews of Modern Physics · doi:10.1103/revmodphys.91.015006 · Cited by 3,722
Photonic Floquet topological insulators
Rechtsman, M. C., Zeuner, J. M., Plotnik, Y., Lumer, Y., Podolsky, D., Dreisow, F., Nolte, S., Segev, M., & Szameit, A. (2013) · Nature · doi:10.1038/nature12066 · Cited by 3,332
Making sense of non-Hermitian Hamiltonians
Bender, C. M. (2007) · Reports on Progress in Physics · doi:10.1088/0034-4885/70/6/r03 · Cited by 2,984
Quantum statistical mechanics in a closed system
Deutsch, J. M. (1991) · Physical Review A · doi:10.1103/physreva.43.2046 · Cited by 2,860
Discretizing light behaviour in linear and nonlinear waveguide lattices
Christodoulides, D. N., Lederer, F., & Silberberg, Y. (2003) · Nature · doi:10.1038/nature01936 · Cited by 1,692
Quantum random walks
Aharonov, Y., Davidovich, L., & Zagury, N. (1993) · Physical Review A · doi:10.1103/physreva.48.1687 · Cited by 1,622
Reflection-Free One-Way Edge Modes in a Gyromagnetic Photonic Crystal
Wang, Z., Chong, Y. D., Joannopoulos, J. D., & Soljačić, M. (2008) · Physical Review Letters · doi:10.1103/physrevlett.100.013905 · Cited by 1,444
Experimental observation of Weyl points
Lu, L., Wang, Z., Ye, D., Ran, L., Fu, L., Joannopoulos, J. D., & Soljačić, M. (2015) · Science · doi:10.1126/science.aaa9273 · Cited by 1,067
Topolectrical-circuit realization of topological corner modes
Imhof, S., Berger, C., Bayer, F., Brehm, J., Molenkamp, L. W., Kiessling, T., Schindler, F., Lee, C. H., Greiter, M., Neupert, T., et al. (2018) · Nature Physics · doi:10.1038/s41567-018-0246-1 · Cited by 1,034
Topological mechanics
Huber, S. D. (2016) · Nature Physics · doi:10.1038/nphys3801 · Cited by 738
Observation of a Topological Transition in the Bulk of a Non-Hermitian System
Zeuner, J. M., Rechtsman, M. C., Plotnik, Y., Lumer, Y., Nolte, S., Rudner, M. S., Segev, M., & Szameit, A. (2015) · Physical Review Letters · doi:10.1103/physrevlett.115.040402 · Cited by 730
Topological Crystalline Insulators and Topological Superconductors: From Concepts to Materials
Ando, Y., & Fu, L. (2015) · Annual Review of Condensed Matter Physics · doi:10.1146/annurev-conmatphys-031214-014501 · Cited by 723
Quantum-optical analogies using photonic structures
Longhi, S. (2009) · Laser & Photonics Reviews · doi:10.1002/lpor.200810055 · Cited by 718 · cited 1×
“Coupled waveguides provide another versatile setting that, instead of simulating static properties, directly emulates the time evolution of tailor-made lattice models (Davis et al. , 1996; Christodoulides, Lederer, and Silberberg, 2003; Longhi, 2009).”
Quantum Walk in Position Space with Single Optically Trapped Atoms
Karski, M., Förster, L., Choi, J.-M., Steffen, A., Alt, W., Meschede, D., & Widera, A. (2009) · Science · doi:10.1126/science.1174436 · Cited by 659
Discrete optics in femtosecond-laser-written photonic structures
Szameit, A., & Nolte, S. (2010) · Journal of Physics B: Atomic, Molecular and Optical Physics · doi:10.1088/0953-4075/43/16/163001 · Cited by 610 · cited 1×
“Photonic crystals belong to the larger experimental platform of optical microresonators, also known as microcavities (Vahala, 2003).”
Background
Observation of topologically protected bound states in photonic quantum walks
Kitagawa, T., Broome, M. A., Fedrizzi, A., Rudner, M. S., Berg, E., Kassal, I., Aspuru-Guzik, A., Demler, E., & White, A. G. (2012) · Nature Communications · doi:10.1038/ncomms1872 · Cited by 607
Photons Walking the Line: A Quantum Walk with Adjustable Coin Operations
Schreiber, A., Cassemiro, K. N., Potoček, V., Gábris, A., Mosley, P. J., Andersson, E., Jex, I., & Silberhorn, C. (2010) · Physical Review Letters · doi:10.1103/physrevlett.104.050502 · Cited by 588
Observation of topological edge states in parity–time-symmetric quantum walks
Xiao, L., Zhan, X., Bian, Z. H., Wang, K. K., Zhang, X., Wang, X. P., Li, J., Mochizuki, K., Kim, D., Kawakami, N., et al. (2017) · Nature Physics · doi:10.1038/nphys4204 · Cited by 576
Exploring topological phases with quantum walks
Kitagawa, T., Rudner, M. S., Berg, E., & Demler, E. (2010) · Physical Review A · doi:10.1103/physreva.82.033429 · Cited by 534
Discrete Single-Photon Quantum Walks with Tunable Decoherence
Broome, M. A., Fedrizzi, A., Lanyon, B. P., Kassal, I., Aspuru-Guzik, A., & White, A. G. (2010) · Physical Review Letters · doi:10.1103/physrevlett.104.153602 · Cited by 420
Chiral Voltage Propagation and Calibration in a Topolectrical Chern Circuit
Hofmann, T., Helbig, T., Lee, C. H., Greiter, M., & Thomale, R. (2019) · Physical Review Letters · doi:10.1103/physrevlett.122.247702 · Cited by 315
Experimental observation of optical Weyl points and Fermi arc-like surface states
Noh, J., Huang, S., Leykam, D., Chong, Y. D., Chen, K. P., & Rechtsman, M. C. (2017) · Nature Physics · doi:10.1038/nphys4072 · Cited by 314
PT-symmetry in honeycomb photonic lattices
Szameit, A., Rechtsman, M. C., Bahat-Treidel, O., & Segev, M. (2011) · Physical Review A · doi:10.1103/physreva.84.021806 · Cited by 280
Weyl and Dirac Semimetals in Three Dimensional Solids
Armitage, N. P., Mele, E. J., & Vishwanath, A. (2017) · arXiv · cited 8×
“…difference from their Hermitian counterpart is that NH Fermi arcs are a bulk phenomenon (similar in this regard to standard Fermi surfaces), while the surface Fermi arcs in 3D Weyl semimetals connect the projection of the Weyl points to a given surface (Armitage, Mele, and Vishwanath, 2018).”
Influential

Flagged first, then by citations

Research works printed but not linked: 289

10.1103/PhysRevLett.114.173902 · DOI · Paper page
10.1103/PhysRevB.55.1142 · DOI · Paper page
10.1103/PhysRevB.86.195414 · DOI · Paper page
10.1103/PhysRevLett.118.174301 · DOI
10.1038/s42005-019-0231-8 · DOI
10.1126/science.aao4551 · DOI · Paper page
10.1126/science.aar4005 · DOI · Paper page
10.1103/PhysRevB.93.020502 · DOI · Paper page
10.1088/1367-2630/15/8/085001 · DOI
10.1103/PhysRevA.96.033846 · DOI
10.1103/PhysRevLett.110.164102 · DOI
10.1103/PhysRevA.88.063631 · DOI
10.1103/PhysRevLett.80.5243 · DOI
10.1103/PhysRevResearch.1.012003 · DOI
Bernard, D., 2002, Statistical Field Theories
10.1023/B:CJOP.0000044002.05657.04 · DOI
10.1088/0305-4470/31/8/019 · DOI
10.1038/natrevmats.2017.66 · DOI · Paper page
10.1103/PhysRevB.96.201305 · DOI
10.1103/PhysRevLett.123.183601 · DOI
10.1038/s41467-019-08397-6 · DOI
10.1103/PhysRevLett.124.056802 · DOI
10.1038/s41467-019-12599-3 · DOI
10.1103/PhysRev.49.519 · DOI
10.1088/1751-8113/47/3/035305 · DOI · Paper page
10.1103/PhysRevB.56.R4333 · DOI
10.1103/PhysRevB.100.161105 · DOI
10.1103/PhysRevLett.125.180403 · DOI
10.1103/PhysRevB.99.041406 · DOI
10.1002/pssr.201206416 · DOI
10.1103/PhysRevA.91.042117 · DOI
10.1038/ncomms11439 · DOI · Paper page
10.1103/PhysRevResearch.2.013078 · DOI
10.1103/PhysRevA.98.042114 · DOI
10.1103/PhysRevB.99.161115 · DOI
Carmichael, H., 2014, An Open Systems Approach to Quantum Optics Lectures Presented at the Université Libre de Bruxelles, October 28 to November 4, 1991
10.1038/s41566-019-0453-z · DOI
10.1073/pnas.1405969111 · DOI
10.1038/nature23281 · DOI · Paper page
10.1103/PhysRevB.87.155114 · DOI
10.1103/PhysRevB.98.245130 · DOI
10.1103/RevModPhys.88.035005 · DOI · Paper page
10.1103/PhysRevResearch.2.022051 · DOI
Datta, S., 2005, Quantum Transport: Atom to Transistor, 10.1017/CBO9781139164313 · DOI
10.1364/OL.21.001729 · DOI · Paper page
10.1088/1751-8113/45/2/025303 · DOI
10.1103/PhysRevB.100.035102 · DOI
10.1142/S0129055X1950003X · DOI
10.1038/nphys1073 · DOI
10.1038/nphys2106 · DOI
10.1038/nature18605 · DOI
10.1103/RevModPhys.89.011004 · DOI
10.1103/PhysRevB.99.081302 · DOI
10.1103/PhysRevResearch.2.043046 · DOI
10.1103/PhysRevLett.79.491 · DOI
10.1103/PhysRevB.56.9630 · DOI
10.1038/nphys4323 · DOI
10.1038/s41566-019-0519-y · DOI
10.1103/PhysRevB.84.205128 · DOI
10.1103/PhysRevB.100.165419 · DOI
10.1103/PhysRevB.100.081401 · DOI
10.1103/PhysRevB.99.121411 · DOI
10.1103/PhysRevB.99.201411 · DOI
10.1103/PhysRev.124.1866 · DOI
10.1038/s41566-017-0031-1 · DOI
10.1126/science.1258479 · DOI
10.1038/nmat3495 · DOI
10.1016/0003-4916(58)90007-1 · DOI
10.1103/PhysRev.96.448 · DOI
10.1016/0003-4916(63)90068-X · DOI
10.1038/ncomms6905 · DOI
10.1103/PhysRevX.7.031023 · DOI · Paper page
10.1088/2515-7639/ab4092 · DOI
10.1103/PhysRevLett.106.106802 · DOI · Paper page
10.1103/PhysRevLett.115.245302 · DOI
10.1073/pnas.2010580117 · DOI
10.1103/PhysRevB.97.014512 · DOI
10.21468/SciPostPhys.7.5.067 · DOI
10.1103/PhysRevX.8.031079 · DOI
10.1103/PhysRevB.96.045437 · DOI
10.1117/12.239858 · DOI
10.1103/PhysRevLett.103.093902 · DOI
10.1103/PhysRevLett.100.013904 · DOI · Paper page
10.1103/PhysRevResearch.2.033018 · DOI
10.1126/science.aar4003 · DOI · Paper page
10.1103/RevModPhys.82.3045 · DOI · Paper page
10.1080/00268976.2019.1593535 · DOI
10.1103/PhysRevLett.77.570 · DOI
10.1103/PhysRevB.56.8651 · DOI
10.1038/s41586-018-0367-9 · DOI
10.1038/ncomms4698 · DOI
10.1088/1751-8113/45/44/444016 · DOI
10.1038/s41567-020-0922-9 · DOI
10.1103/PhysRevA.99.052118 · DOI
10.21468/SciPostPhys.7.5.069 · DOI
10.1103/PhysRevLett.123.190403 · DOI
10.1103/PhysRevResearch.2.023235 · DOI
10.1038/nature23280 · DOI
10.1126/science.1258480 · DOI
10.1103/PhysRevResearch.2.023265 · DOI
10.1103/PhysRevA.102.032216 · DOI
10.1103/PhysRevB.84.153101 · DOI · Paper page
10.1103/PhysRevB.100.165430 · DOI
Joannopoulos, J. D., 2008, Photonic Crystals: Molding the Flow of Light, 10.1515/9781400828241 · DOI
10.1088/1751-8113/45/13/135306 · DOI
10.1038/nphys2835 · DOI
Kato, T., 1966, Perturbation theory of linear operators
10.1103/PhysRevLett.123.066405 · DOI
10.1038/s41467-018-08254-y · DOI
10.1103/PhysRevB.101.195147 · DOI
10.1103/PhysRevX.9.041015 · DOI
Keldysh, L. V., 1964, Sov. Phys. JETP, 20, 1018
10.1103/PhysRevB.94.035137 · DOI
10.1007/s00220-015-2512-8 · DOI
10.1103/PhysRevB.100.115124 · DOI
10.1063/1.3149495 · DOI · Paper page
10.1364/OL.20.001515 · DOI
10.1140/epjd/e2020-100641-y · DOI
10.1016/0024-3795(94)90432-4 · DOI
10.1038/s41467-018-08104-x · DOI
10.1364/OPEX.13.003068 · DOI
10.1103/PhysRevB.99.245116 · DOI
10.1103/PhysRevLett.121.026808 · DOI
10.1103/PhysRevLett.71.2022 · DOI
10.1103/PhysRevA.98.023805 · DOI
10.1038/s42005-018-0035-2 · DOI · Paper page
10.1103/PhysRevLett.123.016805 · DOI
10.1103/PhysRevB.102.085151 · DOI
10.1103/PhysRevB.99.201103 · DOI
10.1103/PhysRevB.101.121109 · DOI
10.1103/PhysRevLett.123.206404 · DOI
10.1103/PhysRevLett.116.133903 · DOI
10.1016/S0921-5107(97)00080-9 · DOI
10.1103/PhysRevLett.118.040401 · DOI
10.1038/s42005-019-0235-4 · DOI · Paper page
10.1103/PhysRevLett.124.250402 · DOI
10.1103/PhysRevB.97.045106 · DOI
10.1103/PhysRevB.98.115135 · DOI
10.1103/PhysRevLett.124.040401 · DOI
10.1103/PhysRevLett.106.213901 · DOI
10.1103/PhysRevB.100.144106 · DOI
10.1103/PhysRevB.99.125103 · DOI
10.1103/PhysRevB.102.235151 · DOI
10.1103/PhysRevLett.122.076801 · DOI
10.1088/1751-8113/44/48/485302 · DOI
10.1002/andp.201800023 · DOI
10.1002/andp.201900054 · DOI
10.1364/OL.44.005804 · DOI
10.1103/PhysRevResearch.1.023013 · DOI
10.1063/1.5028453 · DOI
10.1038/srep13376 · DOI
10.1038/nphoton.2013.42 · DOI
10.1103/PhysRevLett.82.5233 · DOI
10.1103/PhysRevLett.85.1572 · DOI
10.1103/PhysRevResearch.1.033051 · DOI
10.1103/PhysRevLett.123.073601 · DOI
10.1007/BF02959473 · DOI
10.1007/BF02959482 · DOI
10.1103/PhysRevLett.115.200402 · DOI · Paper page
10.1103/PhysRevA.98.033807 · DOI
10.1209/0295-5075/110/67005 · DOI
10.1140/epjst/e2018-800091-5 · DOI
10.1103/PhysRevB.97.121401 · DOI
10.1103/PhysRevLett.125.260601 · DOI
10.1103/PhysRevB.100.100405 · DOI
10.1103/PhysRevX.8.041031 · DOI
10.1103/PhysRevLett.124.196401 · DOI
10.1103/PhysRevB.101.085122 · DOI
10.1126/science.aar7709 · DOI
10.1103/PhysRevLett.110.233902 · DOI
10.1103/PhysRevA.93.062116 · DOI
10.1103/PhysRevLett.120.146601 · DOI
10.1103/PhysRevB.99.041116 · DOI
10.1063/1.1418246 · DOI
10.1038/ncomms9682 · DOI
10.1103/PhysRevB.102.081115 · DOI
10.1073/pnas.1507413112 · DOI
10.1103/PhysRevE.58.1383 · DOI
10.1103/PhysRevX.5.021031 · DOI
10.1038/s41566-018-0179-3 · DOI · Paper page
10.1103/PhysRevB.99.041202 · DOI
10.1103/PhysRevLett.124.086801 · DOI
10.1088/2040-8978/16/6/065501 · DOI
10.1038/s41566-019-0523-2 · DOI
10.1038/s41563-019-0304-9 · DOI
10.1103/PhysRevLett.85.2737 · DOI
10.1007/BF03053496 · DOI
10.1103/PhysRevLett.120.113901 · DOI · Paper page
10.1038/nphys3185 · DOI
10.1038/ncomms10779 · DOI · Paper page
10.1103/PhysRevX.6.041026 · DOI
10.1038/nphys2927 · DOI
10.1073/pnas.1603318113 · DOI
10.1103/PhysRevB.98.155430 · DOI
10.1134/S0021364011210090 · DOI
10.1103/PhysRevB.87.235421 · DOI
10.1038/ncomms7710 · DOI
10.1103/PhysRevLett.122.143901 · DOI
10.1103/PhysRevE.86.066205 · DOI
10.1103/PhysRevLett.103.248101 · DOI

200 of 289 shown

Sorted by citations

A second wave of topological phenomena in photonics and acoustics
Zhang, X., Zangeneh-Nejad, F., Chen, Z.-G., Lu, M.-H., & Christensen, J. (2023) · Nature · doi:10.1038/s41586-023-06163-9 · Cited by 240
Synthetic Non-Abelian Gauge Fields for Non-Hermitian Systems
Pang, Z., Wong, B. T. T., Hu, J., & Yang, Y. (2024) · Physical Review Letters · doi:10.1103/physrevlett.132.043804 · Cited by 41
Truncation-dependent PT phase transition for the edge states of a two-dimensional non-Hermitian system
Cheng, D., Peng, B., Xiao, M., Chen, X., Yuan, L., & Fan, S. (2022) · Physical Review B · doi:10.1103/physrevb.105.l201105 · Cited by 17
Non-Hermitian interacting quantum walks of correlated photons
Wan, T., & Yang, Z. (2025) · Communications Physics · doi:10.1038/s42005-025-02038-9 · Cited by 3

Authors: Bergholtz, E. J., Budich, J. C., & Kunst, F. K.
Venue: Reviews of Modern Physics
Publisher: American Physical Society (APS)
Published: 2021-02-24
Volume: 93
Issue: 1
ISSN: 0034-6861
1539-0756
DOI: 10.1103/revmodphys.93.015005
Cited by: 1,711
References: 28
Language: en
Licence: link.aps.org/licenses/aps-default-license (vor)
Funders: Knut och Alice Wallenbergs Stiftelse
Deutsche Forschungsgemeinschaft (247310070, 39085490)
Vetenskapsrådet
Max Planck Institute of Quantum Optics
Max-Planck-Harvard Research Center for Quantum Optics

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review

Exceptional topology of non-Hermitian systems

Overview

Integrity signals

Verification

Claims the paper makes

Claims other papers make about this one

Self-check

Citations

Cites

Cited by

Metadata

Record

About these checks