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This work introduces a new class of robust states known as Exceptional Boundary (EB) states, which are distinct from the well-known topological and non-Hermitian skin boundary states.
1910
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1912
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Carl M. Bender and Stefan Boettcher, “Real spectra in non-hermitian hamiltonians having p t pt symmetry,” Physical Review Letters 80
1998
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WD Heiss and HL Harney, “The chirality of exceptional points,” The European Physical Journal D-Atomic, Molecular, Optical and Plasma Physics 17
2001
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2001
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Ingo Peschel, “Calculation of reduced density matrices from correlation functions,” Journal of Physics A: Mathematical and General 36
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Michael V Berry, “Physics of nonhermitian degeneracies,” Czechoslovak journal of physics 54
2004
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2004
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Charles L Kane and Eugene J Mele, “Quantum spin hall effect in graphene,” Physical review letters 95
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2007
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Carl M Bender, “Making sense of non-hermitian hamiltonians,” Reports on Progress in Physics 70
2007
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Xiao-Liang Qi, Taylor L Hughes, and Shou-Cheng Zhang, “Topological field theory of time-reversal invariant insulators,” Physical Review B 78
2008
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YL Chen, James G Analytis, J-H Chu, ZK Liu, S-K Mo, Xiao-Liang Qi, HJ Zhang, DH Lu, Xi Dai, Zhong Fang, et al. , “Experimental realization of a three-dimensional topological insulator, bi2te3,” science 325
2009
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Ingrid Rotter, “A non-hermitian hamilton operator and the physics of open quantum systems,” Journal of Physics A: Mathematical and Theoretical 42
2009
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L Jin and Z Song, “Solutions of p t-symmetric tight-binding chain and its equivalent hermitian counterpart,” Physical Review A 80
2009
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M Zahid Hasan and Charles L Kane, “Colloquium: topological insulators,” Rev. Mod. Phys. 82
2010
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Stefano Longhi, “Pt-symmetric laser absorber,” Physical Review A 82
2010
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Lukasz Fidkowski, “Entanglement spectrum of topological insulators and superconductors,” Physical review letters 104
2010
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Ari M Turner, Yi Zhang, and Ashvin Vishwanath, “Entanglement and inversion symmetry in topological insulators,” Physical Review B 82
2010
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Xiao-Liang Qi and Shou-Cheng Zhang, “Topological insulators and superconductors,” Rev. Mod. Phys. 83
2011
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Zhong Wang, Xiao-Liang Qi, and Shou-Cheng Zhang, “Topological field theory and thermal responses of interacting topological superconductors,” Physical Review B 84
2011
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Netanel H Lindner, Gil Refael, and Victor Galitski, “Floquet topological insulator in semiconductor quantum wells,” Nature Physics 7
2011
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N. Moiseyev, “Non-hermitian quantum mechanics,” Cambridge University Press (2011)
2011
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Aris Alexandradinata, Taylor L Hughes, and B Andrei Bernevig, “Trace index and spectral flow in the entanglement spectrum of topological insulators,” Physical Review B 84
2011
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WD Heiss, “The physics of exceptional points,” Journal of Physics A: Mathematical and Theoretical 45
2012
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Soo-Young Lee, Jung-Wan Ryu, Sang Wook Kim, and Yunchul Chung, “Geometric phase around multiple exceptional points,” Physical Review A 85
2012
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Xiao-Liang Qi, Hosho Katsura, and Andreas WW Ludwig, “General relationship between the entanglement spectrum and the edge state spectrum of topological quantum states,” Physical review letters 108
2012
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Dorje C Brody and Eva-Maria Graefe, “Information geometry of complex hamiltonians and exceptional points,” Entropy 15
2013
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Dorje C Brody, “Biorthogonal quantum mechanics,” Journal of Physics A: Mathematical and Theoretical 47
2013
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AR Mellnik, JS Lee, A Richardella, JL Grab, PJ Mintun, Mark H Fischer, Abolhassan Vaezi, Aurelien Manchon, E-A Kim, N Samarth, et al. , “Spin-transfer torque generated by a topological insulator,” Nature 511
2014
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Ching Hua Lee and Peng Ye, “Free-fermion entanglement spectrum through wannier interpolation,” Physical Review B 91
2015
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Tony E. Lee, “Anomalous edge state in a non-hermitian lattice,” Physical Review Letters 116
2016
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Haitan Xu, David Mason, Luyao Jiang, and JGE Harris, “Topological energy transfer in an optomechanical system with exceptional points,” Nature 537
2016
Cited alongside, same era.
P Wang, L Jin, G Zhang, and Z Song, “Wave emission and absorption at spectral singularities,” Physical Review A 94
2016
Cited alongside, same era.
Ching Hua Lee, Daniel P Arovas, and Ronny Thomale, “Band flatness optimization through complex analysis,” Physical Review B 93
2016
Cited alongside, same era.
Absar U. Hassan, Bo Zhen, Marin Soljačić, Mercedeh Khajavikhan, and Demetrios N. Christodoulides, “Dynamically encircling exceptional points: Exact evolution and polarization state conversion,” Physical Review Letters 118
2017
Cited alongside, same era.
Wenchao Hu, Hailong Wang, Perry Ping Shum, and Y. D. Chong, “Exceptional points in a non-hermitian topological pump,” Physical Review B 95
M Naghiloo, M Abbasi, Yogesh N Joglekar, and KW Murch, “Quantum state tomography across the exceptional point in a single dissipative qubit,” Nature Physics 15
2019
Later among the works it cites.
ŞK Özdemir, S Rotter, F Nori, and L Yang, “Parity–time symmetry and exceptional points in photonics,” Nature materials 18
2019
Later among the works it cites.
Balázs Dóra, Markus Heyl, and Roderich Moessner, “The kibble-zurek mechanism at exceptional points,” Nature communications 10
2019
Later among the works it cites.
Loïc Herviou, Nicolas Regnault, and Jens H Bardarson, “Entanglement spectrum and symmetries in non-hermitian fermionic non-interacting models,” SciPost Phys. 7
2019
Later among the works it cites.
Dan S. Borgnia, Alex Jura Kruchkov, and Robert-Jan Slager, “Non-hermitian boundary modes and topology,” Physical Review Letters 124
2020
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2017
Cited alongside, same era.
Weijian Chen, Şahin Kaya Özdemir, Guangming Zhao, Jan Wiersig, and Lan Yang, “Exceptional points enhance sensing in an optical microcavity,” Nature 548
2017
Cited alongside, same era.
Ching Hua Lee, Martin Claassen, and Ronny Thomale, “Band structure engineering of ideal fractional chern insulators,” Physical Review B 96
2017
Cited alongside, same era.
Ye Xiong, “Why does bulk boundary correspondence fail in some non-hermitian topological models,” Journal of Physics Communications 2
2018
Cited alongside, same era.
Shunyu Yao and Zhong Wang, “Edge states and topological invariants of non-hermitian systems,” Physical Review Letters 121
2018
Cited alongside, same era.
Flore K. Kunst, Elisabet Edvardsson, Jan Carl Budich, and Emil J. Bergholtz, “Biorthogonal bulk-boundary correspondence in non-hermitian systems,” Physical Review Letters 121
2018
Cited alongside, same era.
2018
Cited alongside, same era.
Zongping Gong, Yuto Ashida, Kohei Kawabata, Kazuaki Takasan, Sho Higashikawa, and Masahito Ueda, “Topological phases of non-hermitian systems,” Physical Review X 8
2018
Cited alongside, same era.
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Matheus IN Rosa and Massimo Ruzzene, “Dynamics and topology of non-hermitian elastic lattices with non-local feedback control interactions,” New Journal of Physics 22
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Lei Xiao, Tianshu Deng, Kunkun Wang, Gaoyan Zhu, Zhong Wang, Wei Yi, and Peng Xue, “Non-hermitian bulk–boundary correspondence in quantum dynamics,” Nature Physics , 1–6 (2020)
2020
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Nobuyuki Okuma, Kohei Kawabata, Ken Shiozaki, and Masatoshi Sato, “Topological origin of non-hermitian skin effects,” Physical Review Letters 124
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Rebekka Koch and Jan Carl Budich, “Bulk-boundary correspondence in non-hermitian systems: stability analysis for generalized boundary conditions,” The European Physical Journal D 74
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Wei Xin Teo Teo, Linhu Li, Xizheng Zhang, and Jiangbin Gong, “Topological characterization of non-hermitian multiband systems using majorana’s stellar representation,” Physical Review B 101
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Xizheng Zhang and Jiangbin Gong, “Non-hermitian floquet topological phases: Exceptional points, coalescent edge modes, and the skin effect,” Physical Review B 101
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Jan Wiersig, “Prospects and fundamental limits in exceptional point-based sensing,” Nature Communications 11
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Heming Wang, Yu-Hung Lai, Zhiquan Yuan, Myoung-Gyun Suh, and Kerry Vahala, “Petermann-factor sensitivity limit near an exceptional point in a brillouin ring laser gyroscope,” Nature communications 11
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