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Frontiers of Physics

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Front. Phys.    2022, Vol. 17 Issue (3) : 33502    https://doi.org/10.1007/s11467-021-1126-1
RESEARCH ARTICLE
Biorthogonal quantum criticality in non-Hermitian many-body systems
Gaoyong Sun1,2(), Jia-Chen Tang1,2, Su-Peng Kou3()
1. College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China
2. Key Laboratory of Aerospace Information Materials and Physics(Nanjing University of Aeronautics and Astronautics), MIIT, Nanjing 211106, China
3. Center for Advanced Quantum Studies, Department of Physics, Beijing Normal University, Beijing 100875, China
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Abstract

We develop the perturbation theory of the fidelity susceptibility in biorthogonal bases for arbitrary interacting non-Hermitian many-body systems with real eigenvalues. The quantum criticality in the non-Hermitian transverse field Ising chain is investigated by the second derivative of the ground-state energy and the ground-state fidelity susceptibility. We show that the system undergoes a second-order phase transition with the Ising universal class by numerically computing the critical points and the critical exponents from the finite-size scaling theory. Interestingly, our results indicate that the biorthogonal quantum phase transitions are described by the biorthogonal fidelity susceptibility instead of the conventional fidelity susceptibility.
Keywords biorthogonal quantum criticality      non-Hermitian systems      fidelity susceptibility     
Corresponding Author(s): Gaoyong Sun,Su-Peng Kou   
Issue Date: 23 November 2021
 Cite this article:   
Gaoyong Sun,Jia-Chen Tang,Su-Peng Kou. Biorthogonal quantum criticality in non-Hermitian many-body systems[J]. Front. Phys. , 2022, 17(3): 33502.
 URL:  
https://academic.hep.com.cn/fop/EN/10.1007/s11467-021-1126-1
https://academic.hep.com.cn/fop/EN/Y2022/V17/I3/33502
1 S. Sachdev , Quantum Phase Transitions, Cambridge University Press, 1999
2 M. Levin and X. G. Wen , Detecting topological order in a ground state wave function, Phys. Rev. Lett. 96 (11), 110405 (2006)
https://doi.org/10.1103/PhysRevLett.96.110405
3 M. E. Fisher and M. N. Barber , Scaling theory for finitesize effects in the critical region, Phys. Rev. Lett. 28, 1516 (1972)
https://doi.org/10.1103/PhysRevLett.28.1516
4 M. E. Fisher , The renormalization group in the theory of critical behavior, Rev. Mod. Phys. 46 (4), 597 (1974)
https://doi.org/10.1103/RevModPhys.46.597
5 E. J. Bergholtz , J. C. Budich , and F. K. Kunst , Exceptional topology of non-Hermitian systems, Rev. Mod. Phys. 93 (1), 015005 (2021)
https://doi.org/10.1103/RevModPhys.93.015005
6 Y. Ashida , Z. Gong , and M. Ueda , Non-Hermitian physics, Adv. Phys. 69 (3), 249 (2020)
https://doi.org/10.1080/00018732.2021.1876991
7 T. E. Lee , Anomalous edge state in a non-Hermitian lattice, Phys. Rev. Lett. 116 (13), 133903 (2016)
https://doi.org/10.1103/PhysRevLett.116.133903
8 S. Yao , and Z. Wang , Edge states and topological invariants of non-Hermitian systems, Phys. Rev. Lett. 121 (8), 086803 (2018)
https://doi.org/10.1103/PhysRevLett.121.086803
9 F. K. Kunst , E. Edvardsson , J. C. Budich , and E. J. Bergholtz , Biorthogonal bulk-boundary correspondence in non-Hermitian systems, Phys. Rev. Lett. 121 (2), 026808 (2018)
https://doi.org/10.1103/PhysRevLett.121.026808
10 Y. Xiong , Why does bulk boundary correspondence fail in some non-Hermitian topological models, J. Phys. Commun. 2 (3), 035043 (2018)
https://doi.org/10.1088/2399-6528/aab64a
11 Z. Gong , Y. Ashida , K. Kawabata , K. Takasan , S. Higashikawa , and M. Ueda , Topological phases of nonHermitian systems, Phys. Rev. X 8 (3), 031079 (2018)
https://doi.org/10.1103/PhysRevX.8.031079
12 V. M. M. Alvarez , J. E. B. Vargas , and L. E. F. F. Torres , Non-Hermitian robust edge states in one dimension: Anomalous localization and eigenspace condensation at exceptional points, Phys. Rev. B 97, 121401(R) (2018)
https://doi.org/10.1103/PhysRevB.97.121401
13 K. Yokomizo and S. Murakami , Non-Bloch band theory of non-Hermitian systems, Phys. Rev. Lett. 123 (6), 066404 (2019)
https://doi.org/10.1103/PhysRevLett.123.066404
14 N. Okuma , K. Kawabata , K. Shiozaki , and M. Sato , Topological origin of non-Hermitian skin effects, Phys. Rev. Lett. 124 (8), 086801 (2020)
https://doi.org/10.1103/PhysRevLett.124.086801
15 K. Zhang , Z. Yang , and C. Fang , Correspondence between winding numbers and skin modes in non-Hermitian systems, Phys. Rev. Lett. 125 (12), 126402 (2020)
https://doi.org/10.1103/PhysRevLett.125.126402
16 Z. Yang , K. Zhang , C. Fang , and J. Hu , Non-Hermitian bulk-boundary correspondence and auxiliary generalized Brillouin zone theory, Phys. Rev. Lett. 125 (22), 226402 (2020)
https://doi.org/10.1103/PhysRevLett.125.226402
17 X.-R. Wang , C.-X. Guo , and S.-P. Kou , Defective edge states and number-anomalous bulk-boundary correspondence in non-Hermitian topological systems, Phys. Rev. B 101, 121116(R) (2020)
https://doi.org/10.1103/PhysRevB.101.121116
18 H. Jiang , R. Lü , and S. Chen , Topological invariants , zero mode edge states and finite size effect for a generalized non-reciprocal Su–Schrieffer–Heeger model, Eur. Phys. J. B 93 (7), 125 (2020)
https://doi.org/10.1140/epjb/e2020-10036-3
19 S. Weidemann , M. Kremer , T. Helbig , T. Hofmann , A. Stegmaier , M. Greiter , R. Thomale , and A. Szameit , Topological funneling of light, Science 368 (6488), 311 (2020)
https://doi.org/10.1126/science.aaz8727
20 L. Xiao , T. Deng , K. Wang , G. Zhu , Z. Wang , W. Yi , and P. Xue , Observation of non-Hermitian bulk-boundary correspondence in quantum dynamics, Nat. Phys. 16, 761 (2020)
https://doi.org/10.1038/s41567-020-0836-6
21 D. S. Borgnia , A. J. Kruchkov , and R. J. Slager , NonHermitian boundary modes and topology, Phys. Rev. Lett. 124 (5), 056802 (2020)
https://doi.org/10.1103/PhysRevLett.124.056802
22 W. Heiss , The physics of exceptional points, J. Phys. A Math. Theor. 45 (44), 444016 (2012)
https://doi.org/10.1088/1751-8113/45/44/444016
23 V. Kozii and L. Fu , Non-Hermitian topological theory of finite-lifetime quasiparticles: Prediction of bulk Fermi arc due to exceptional point, arXiv: 1708.05841 (2017)
24 H. Hodaei , A. U. Hassan , S. Wittek , H. Garcia-Gracia , R. El-Ganainy , D. N. Christodoulides , and M. Khajavikhan , Enhanced sensitivity at higher-order exceptional points, Nature 548 (7666), 187 (2017)
https://doi.org/10.1038/nature23280
25 H. Zhou , C. Peng , Y. Yoon , C. W. Hsu , K. A. Nelson , L. Fu , J. D. Joannopoulos , M. Soljacic , and B. Zhen , Observation of bulk Fermi arc and polarization half charge from paired exceptional points, Science 359 (6379), 1009 (2018)
https://doi.org/10.1126/science.aap9859
26 M. A. Miri and A. Alu , Exceptional points in optics and photonics, Science 363 (6422), eaar7709 (2019)
https://doi.org/10.1126/science.aar7709
27 J. H. Park , A. Ndao , W. Cai , L. Y. Hsu , A. Kodigala , T. Lepetit , Y. H. Lo , and B. Kanté , Observation of plasmonic exceptional points, arXiv: 1904.01073 (2019)
28 Z. Yang and J. Hu , Non-Hermitian Hopf-link exceptional line semimetals, Phys. Rev. B 99, 081102(R) (2019)
https://doi.org/10.1103/PhysRevB.99.081102
29 S. Özdemir , S. Rotter , F. Nori , and L. Yang , Parity–time symmetry and exceptional points in photonics, Nat. Mater. 18 (8), 783 (2019)
https://doi.org/10.1038/s41563-019-0304-9
30 B. Dóra , M. Heyl , and R. Moessner , The Kibble–Zurek mechanism at exceptional points, Nat. Commun. 10 (1), 2254 (2019)
https://doi.org/10.1038/s41467-019-10048-9
31 Y. R. Zhang , Z. Z. Zhang , J. Q. Yuan , M. Kang , and J. Chen , High-order exceptional points in non-Hermitian Moiré lattices, Front. Phys. 14 (5), 53603 (2019)
https://doi.org/10.1007/s11467-019-0899-y
32 L. Jin , H. C. Wu , B. B. Wei , and Z. Song , Hybrid exceptional point created from type-Ⅲ Dirac point, Phys. Rev. B 101 (4), 045130 (2020)
https://doi.org/10.1103/PhysRevB.101.045130
33 L. Xiao , T. Deng , K. Wang , Z. Wang , W. Yi , and P. Xue , Observation of non-Bloch parity-time symmetry and exceptional points, Phys. Rev. Lett. 126 (23), 230402 (2021)
https://doi.org/10.1103/PhysRevLett.126.230402
34 N. Matsumoto , K. Kawabata , Y. Ashida , S. Furukawa , and M. Ueda , Continuous phase transition without gap closing in non-Hermitian quantum many-body systems, Phys. Rev. Lett. 125 (26), 260601 (2020)
https://doi.org/10.1103/PhysRevLett.125.260601
35 M. L. Yang , H. Wang , C. X. Guo , X. R. Wang , G. Sun , and S. P. Kou , Anomalous spontaneous symmetry breaking in non-Hermitian systems with biorthogonal Z2-symmetry, arXiv: 2006.10278 (2020)
36 L. Jin and Z. Song , Scaling behavior and phase diagram of a PT-symmetric non-Hermitian Bose–Hubbard system, Ann. Phys. 330, 142 (2013)
https://doi.org/10.1016/j.aop.2012.11.017
37 Y. Ashida , S. Furukawa , and M. Ueda , Parity–timesymmetric quantum critical phenomena, Nat. Commun. 8 (1), 15791 (2017)
https://doi.org/10.1038/ncomms15791
38 L. Herviou , N. Regnault , and J. H. Bardarson , Entanglement spectrum and symmetries in non-Hermitian fermionic non-interacting models, SciPost Physics 7 (5), 069 (2019)
https://doi.org/10.21468/SciPostPhys.7.5.069
39 P. Y. Chang , J. S. You , X. Wen , and S. Ryu , Entanglement spectrum and entropy in topological non-Hermitian systems and nonunitary conformal field theory, Phys. Rev. Res. 2 (3), 033069 (2020)
https://doi.org/10.1103/PhysRevResearch.2.033069
40 S. Mu , C. H. Lee , L. Li , and J. Gong , Emergent Fermi surface in a many-body non-Hermitian fermionic chain, Phys. Rev. B 102, 081115(R) (2020)
https://doi.org/10.1103/PhysRevB.102.081115
41 E. Lee , H. Lee , and B.-J. Yang , Many-body approach to non-Hermitian physics in fermionic systems, Phys. Rev. B 101, 121109(R) (2020)
https://doi.org/10.1103/PhysRevB.101.121109
42 L. Pan , X. Chen , Y. Chen , and H. Zhai , Non-Hermitian linear response theory, Nat. Phys. 16 (7), 767 (2020)
https://doi.org/10.1038/s41567-020-0889-6
43 L. Pan , X. Wang , X. Cui , and S. Chen , Interactioninduced dynamical PT-symmetry breaking in dissipative Fermi–Hubbard models, Phys. Rev. A 102 (2), 023306 (2020)
https://doi.org/10.1103/PhysRevA.102.023306
44 Z. Xu and S. Chen , Topological Bose–Mott insulators in one-dimensional non-Hermitian superlattices, Phys. Rev. B 102 (3), 035153 (2020)
https://doi.org/10.1103/PhysRevB.102.035153
45 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–André–Harper model, Phys. Rev. B 101 (23), 235150 (2020)
https://doi.org/10.1103/PhysRevB.101.235150
46 C. H. Lee , Many-body topological and skin states without open boundaries, arXiv: 2006.01182 (2020)
47 H. Shackleton and M. S. Scheurer , Protection of paritytime symmetry in topological many-body systems: NonHermitian toric code and fracton models, Phys. Rev. Res. 2 (3), 033022 (2020)
https://doi.org/10.1103/PhysRevResearch.2.033022
48 T. Liu , J. J. He , T. Yoshida , Z. L. Xiang , and F. Nori , Non-Hermitian topological Mott insulators in one-dimensional fermionic superlattices, Phys. Rev. B 102 (23), 235151 (2020)
https://doi.org/10.1103/PhysRevB.102.235151
49 K. Yang , S. C. Morampudi , and E. J. Bergholtz , Exceptional spin liquids from couplings to the environment, Phys. Rev. Lett. 126 (7), 077201 (2021)
https://doi.org/10.1103/PhysRevLett.126.077201
50 R. Hanai , A. Edelman , Y. Ohashi , and P. B. Littlewood , Non-Hermitian phase transition from a polariton Bose– Einstein condensate to a photon laser, Phys. Rev. Lett. 122 (18), 185301 (2019)
https://doi.org/10.1103/PhysRevLett.122.185301
51 R. Hamazaki , K. Kawabata , and M. Ueda , NonHermitian many-body localization, Phys. Rev. Lett. 123 (9), 090603 (2019)
https://doi.org/10.1103/PhysRevLett.123.090603
52 W. Xi , Z. H. Zhang , Z. C. Gu , and W. Q. Chen , Classification of topological phases in one dimensional interacting non-Hermitian systems and emergent unitarity, Sci. Bull. (Beijing) 66 (17), 1731 (2021)
https://doi.org/10.1016/j.scib.2021.04.027
53 K. Yamamoto , M. Nakagawa , K. Adachi , K. Takasan , M. Ueda , and N. Kawakami , Theory of non-Hermitian fermionic superfluidity with a complex-valued interaction, Phys. Rev. Lett. 123 (12), 123601 (2019)
https://doi.org/10.1103/PhysRevLett.123.123601
54 R. Hanai and P. B. Littlewood , Critical fluctuations at a many-body exceptional point, Phys. Rev. Res. 2 (3), 033018 (2020)
https://doi.org/10.1103/PhysRevResearch.2.033018
55 R. Arouca , C. H. Lee , and C. M. Smith , Unconventional scaling at non-Hermitian critical points, Phys. Rev. B 102 (24), 245145 (2020)
https://doi.org/10.1103/PhysRevB.102.245145
56 P. Zanardi and N. Paunkovic , Ground state overlap and quantum phase transitions, Phys. Rev. E 74 (3), 031123 (2006)
https://doi.org/10.1103/PhysRevE.74.031123
57 L. Campos Venuti and P. Zanardi , Quantum critical scaling of the geometric tensors, Phys. Rev. Lett. 99 (9), 095701 (2007)
https://doi.org/10.1103/PhysRevLett.99.095701
58 W. L. You , Y. W. Li , and S. J. Gu , Fidelity, dynamic structure factor, and susceptibility in critical phenomena, Phys. Rev. E 76 (2), 022101 (2007)
https://doi.org/10.1103/PhysRevE.76.022101
59 A. F. Albuquerque , F. Alet , C. Sire , and S. Capponi , Quantum critical scaling of fidelity susceptibility, Phys. Rev. B 81 (6), 064418 (2010)
https://doi.org/10.1103/PhysRevB.81.064418
60 S. J. Gu , Fidelity approach to quantum phase transitions, Int. J. Mod. Phys. B 24 (23), 4371 (2010)
https://doi.org/10.1142/S0217979210056335
61 G. Sun , Fidelity susceptibility study of quantum longrange antiferromagnetic Ising chain, Phys. Rev. A 96 (4), 043621 (2017)
https://doi.org/10.1103/PhysRevA.96.043621
62 Z. Zhu , G. Sun , W. L. You , and D. N. Shi , Fidelity and criticality of a quantum Ising chain with long-range interactions, Phys. Rev. A 98 (2), 023607 (2018)
https://doi.org/10.1103/PhysRevA.98.023607
63 B. B. Wei and X. C. Lv , Fidelity susceptibility in the quantum Rabi model, Phys. Rev. A 97 (1), 013845 (2018)
https://doi.org/10.1103/PhysRevA.97.013845
64 B. B. Wei , Fidelity susceptibility in one-dimensional disordered lattice models, Phys. Rev. A 99 (4), 042117 (2019)
https://doi.org/10.1103/PhysRevA.99.042117
65 S. Chen , L. Wang , Y. Hao , and Y. Wang , Intrinsic relation between ground-state fidelity and the characterization of a quantum phase transition, Phys. Rev. A 77 (3), 032111 (2008)
https://doi.org/10.1103/PhysRevA.77.032111
66 S. J. Gu , H. M. Kwok , W. Q. Ning , and H. Q. Lin , Fidelity susceptibility, scaling, and universality in quantum critical phenomena, Phys. Rev. B 77 (24), 245109 (2008)
https://doi.org/10.1103/PhysRevB.77.245109
67 S. Yang , S. J. Gu , C. P. Sun , and H. Q. Lin , Fidelity susceptibility and long-range correlation in the Kitaev honeycomb model, Phys. Rev. A 78 (1), 012304 (2008)
https://doi.org/10.1103/PhysRevA.78.012304
68 H. M. Kwok , W. Q. Ning , S. J. Gu , and H. Q. Lin , Quantum criticality of the Lipkin–Meshkov–Glick model in terms of fidelity susceptibility, Phys. Rev. E 78 (3), 032103 (2008)
https://doi.org/10.1103/PhysRevE.78.032103
69 L. Gong and P. Tong , Fidelity, fidelity susceptibility, and von Neumann entropy to characterize the phase diagram of an extended Harper model, Phys. Rev. B 78 (11), 115114 (2008)
https://doi.org/10.1103/PhysRevB.78.115114
70 W. C. Yu , H. M. Kwok , J. Cao , and S. J. Gu , Fidelity susceptibility in the two-dimensional transverse-field Ising and XXZ models, Phys. Rev. E 80 (2), 021108 (2009)
https://doi.org/10.1103/PhysRevE.80.021108
71 D. Schwandt , F. Alet , and S. Capponi , Quantum Monte Carlo simulations of fidelity at magnetic quantum phase transitions, Phys. Rev. Lett. 103 (17), 170501 (2009)
https://doi.org/10.1103/PhysRevLett.103.170501
72 Q. Luo , J. Zhao , and X. Wang , Fidelity susceptibility of the anisotropic XY model: The exact solution, Phys. Rev. E 98 (2), 022106 (2018)
https://doi.org/10.1103/PhysRevE.98.022106
73 M. M. Rams and B. Damski , Quantum fidelity in the thermodynamic limit, Phys. Rev. Lett. 106 (5), 055701 (2011)
https://doi.org/10.1103/PhysRevLett.106.055701
74 S. H. Li , Q. Q. Shi , Y. H. Su , J. H. Liu , Y. W. Dai , and H. Q. Zhou , Tensor network states and ground-state fidelity for quantum spin ladders, Phys. Rev. B 86 (6), 064401 (2012)
https://doi.org/10.1103/PhysRevB.86.064401
75 V. Mukherjee , A. Dutta , and D. Sen , Quantum fidelity for one-dimensional Dirac fermions and two-dimensional Kitaev model in the thermodynamic limit, Phys. Rev. B 85 (2), 024301 (2012)
https://doi.org/10.1103/PhysRevB.85.024301
76 B. Damski , Fidelity susceptibility of the quantum Ising model in a transverse field: The exact solution, Phys. Rev. E 87 (5), 052131 (2013)
https://doi.org/10.1103/PhysRevE.87.052131
77 J. Carrasquilla , S. R. Manmana , and M. Rigol , Scaling of the gap , Scaling of the gap, fidelity susceptibility, and Bloch oscillations across the superfluid-to-Mott-insulator transition in the one-dimensional Bose–Hubbard model, Phys. Rev. A 87 (4), 043606 (2013)
https://doi.org/10.1103/PhysRevA.87.043606
78 M. Łącki , B. Damski , and J. Zakrzewski , Numerical studies of ground-state fidelity of the Bose–Hubbard model, Phys. Rev. A 89 (3), 033625 (2014)
https://doi.org/10.1103/PhysRevA.89.033625
79 G. Sun and T. Vekua , Topological quasi-one-dimensional state of interacting spinless electrons, Phys. Rev. B 93 (20), 205137 (2016)
https://doi.org/10.1103/PhysRevB.93.205137
80 M.-F. Yang , Ground-state fidelity in one-dimensional gapless models, Phys. Rev. B 76, 180403(R) (2007)
https://doi.org/10.1103/PhysRevB.76.180403
81 J. O. Fjærestad , Ground state fidelity of Luttinger liquids: A wavefunctional approach, J. Stat. Mech. 2008 (07), P07011 (2008)
https://doi.org/10.1088/1742-5468/2008/07/P07011
82 A. Langari and A. Rezakhani , Quantum renormalization group for ground-state fidelity, New J. Phys. 14 (5), 053014 (2012)
https://doi.org/10.1088/1367-2630/14/5/053014
83 G. Sun , A. K. Kolezhuk , and T. Vekua , Fidelity at Berezinskii–Kosterlitz–Thouless quantum phase transitions, Phys. Rev. B 91 (1), 014418 (2015)
https://doi.org/10.1103/PhysRevB.91.014418
84 L. Cincio , M. M. Rams , J. Dziarmaga , and W. H. Zurek , Universal shift of the fidelity susceptibility peak away from the critical point of the Berezinskii–Kosterlitz–Thouless quantum phase transition, Phys. Rev. B 100, 081108(R) (2019)
https://doi.org/10.1103/PhysRevB.100.081108
85 G. Sun , B. B. Wei , and S. P. Kou , Fidelity as a probe for a deconfined quantum critical point, Phys. Rev. B 100 (6), 064427 (2019)
https://doi.org/10.1103/PhysRevB.100.064427
86 H. Jiang , C. Yang , and S. Chen , Topological invariants and phase diagrams for one-dimensional two-band nonHermitian systems without chiral symmetry, Phys. Rev. A 98 (5), 052116 (2018)
https://doi.org/10.1103/PhysRevA.98.052116
87 C. Wang , M. L. Yang , C. X. Guo , X. M. Zhao , and S. P. Kou , Effective non-Hermitian physics for degenerate ground states of a non-Hermitian Ising model with RT symmetry, EPL (Europhysics Letters) 128 (4), 41001 (2020)
https://doi.org/10.1209/0295-5075/128/41001
88 C. X. Guo , X. R. Wang , and S. P. Kou , Non-Hermitian avalanche effect: Non-perturbative effect induced by local non-Hermitian perturbation on a Z2 topological order, EPL (Europhysics Letters) 131 (2), 27002 (2020)
https://doi.org/10.1209/0295-5075/131/27002
89 Y. Nishiyama , Imaginary-field-driven phase transition for the 2D Ising antiferromagnet: A fidelity-susceptibility approach, Physica A 555, 124731 (2020)
https://doi.org/10.1016/j.physa.2020.124731
90 Y. Nishiyama , Fidelity-susceptibility analysis of the honeycomb-lattice Ising antiferromagnet under the imaginary magnetic field, Eur. Phys. J. B 93 (9), 174 (2020)
https://doi.org/10.1140/epjb/e2020-10264-5
91 Y. C. Tzeng , C. Y. Ju , G. Y. Chen , and W. M. Huang , Hunting for the non-Hermitian exceptional points with fidelity susceptibility, Phys. Rev. Res. 3 (1), 013015 (2021)
https://doi.org/10.1103/PhysRevResearch.3.013015
92 D. D. Solnyshkov , C. Leblanc , L. Bessonart , A. Nalitov , J. Ren , Q. Liao , F. Li , and G. Malpuech , Quantum metric and wave packets at exceptional points in non-Hermitian systems, Phys. Rev. B 103 (12), 125302 (2021)
https://doi.org/10.1103/PhysRevB.103.125302
93 D. C. Brody , Biorthogonal quantum mechanics, J. Phys. A Math. Theor. 47 (3), 035305 (2014)
https://doi.org/10.1088/1751-8113/47/3/035305
94 M. M. Sternheim and J. F. Walker , Non-Hermitian Hamiltonians, decaying states, and perturbation theory, Phys. Rev. C 6 (1), 114 (1972)
https://doi.org/10.1103/PhysRevC.6.114
95 A. Mostafazadeh , Pseudo-hermiticity versus PT symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian, J. Math. Phys. 43 (1), 205 (2002)
https://doi.org/10.1063/1.1418246
96 A. Mostafazadeh , Pseudo-hermiticity versus PT-symmetry (Ⅱ): A complete characterization of non-Hermitian Hamiltonians with a real spectrum, J. Math. Phys. 43 (5), 2814 (2002)
https://doi.org/10.1063/1.1461427
97 A. Mostafazadeh , Pseudo-hermiticity versus PT-symmetry (Ⅲ): Equivalence of pseudo-hermiticity and the presence of antilinear symmetries, J. Math. Phys. 43 (8), 3944 (2002)
https://doi.org/10.1063/1.1489072
98 Y. Y. Fu , Y. Fei , D. X. Dong , and Y. W. Liu , Photonic spin Hall effect in PT-symmetric metamaterials, Front. Phys. 14 (6), 62601 (2019)
https://doi.org/10.1007/s11467-019-0938-8
99 Y. Zhao , Equivariant PT-symmetric real Chern insulators, Front. Phys. 15 (1), 13603 (2020)
https://doi.org/10.1007/s11467-019-0943-y
100 Y. C. Chen , M. Gong , P. Xue , H. D. Yuan , and C. J. Zhang , Quantum deleting and cloning in a pseudounitary system, Front. Phys. 16 (5), 53601 (2021)
https://doi.org/10.1007/s11467-021-1063-z
101 A. Uhlmann , The “transition probability” in the state space of a ∗-algebra, Rep. Math. Phys. 9 (2), 273 (1976)
https://doi.org/10.1016/0034-4877(76)90060-4
102 M. Hauru and G. Vidal , Uhlmann fidelities from tensor networks, Phys. Rev. A 98 (4), 042316 (2018)
https://doi.org/10.1103/PhysRevA.98.042316
103 G. Gehlen , Critical and off-critical conformal analysis of the Ising quantum chain in an imaginary field, J. Phys. Math. Gen. 24 (22), 5371 (1991)
https://doi.org/10.1088/0305-4470/24/22/021
104 D. Bianchini , O. Castro-Alvaredo , B. Doyon , E. Levi , and F. Ravanini , Entanglement entropy of non-unitary conformal field theory, J. Phys. A Math. Theor. 48 (4), 04FT01 (2015)
https://doi.org/10.1088/1751-8113/48/4/04FT01
105 K. L. Zhang and Z. Song , Ising chain with topological degeneracy induced by dissipation, Phys. Rev. B 101 (24), 245152 (2020)
https://doi.org/10.1103/PhysRevB.101.245152
106 J. Um , S. I. Lee , and B. J. Kim , Quantum phase transition and finite-size scaling of the one-dimensional Ising model, J. Korean Phys. Soc. 50, 285 (2007)
107 W. L. You and W. L. Lu , Scaling of reduced fidelity susceptibility in the one-dimensional transverse-field XY model, Phys. Lett. A 373 (16), 1444 (2009)
https://doi.org/10.1016/j.physleta.2009.02.046
108 N. Hatano and H. Obuse , Delocalization of a nonHermitian quantum walk on random media in one dimension, Ann. Phys. 168615 (2021)
https://doi.org/10.1016/j.aop.2021.168615
109 T. Liu , S. Cheng , H. Guo , and G. Xianlong , Fate of Majorana zero modes, exact location of critical states, and unconventional real-complex transition in non-Hermitian quasiperiodic lattices, Phys. Rev. B 103 (10), 104203 (2021)
https://doi.org/10.1103/PhysRevB.103.104203
110 Q. Lin , T. Li , L. Xiao , K. Wang , W. Yi , and P. Xue , Observation of non-Hermitian topological Anderson insulator in quantum dynamics, arXiv: 2108.01097 (2021)
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