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2025 Volume 34 Issue 5

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Kangyi Hu(胡康溢), Menghua Deng(邓孟华), and Fuxiang Li(李福祥)†. 2025: Exactly solvable models for non-Hermitian systems under nonadiabatic quench dynamics, Chinese Physics B, 34(5): 050204. doi: 10.1088/1674-1056/adbd26

Citation:

Kangyi Hu(胡康溢), Menghua Deng(邓孟华), and Fuxiang Li(李福祥)†. 2025: Exactly solvable models for non-Hermitian systems under nonadiabatic quench dynamics, Chinese Physics B, 34(5): 050204. doi: 10.1088/1674-1056/adbd26

Exactly solvable models for non-Hermitian systems under nonadiabatic quench dynamics

School of Physics and Electronics, Hunan University, Changsha 410082, China

Received Date: 30/11/2024
Accepted Date: 22/01/2025
Fund Project:
Project supported by the National Key Research and Development Program of the Ministry of Science and Technology of China (Grant No. 2021YFA1200700), the National Natural Science Foundation of China (Grant Nos. 11905054 and 12275075), and the Fundamental Research Funds for the Central Universities of China.
PACS: 02.60.-x; 02.60.Jh; 03.65.-w; 33.50.Hv

Abstract

Due to the nonunitary time evolution and possibly complex energy eigenvalues in non-Hermitian systems, it is still under debate how to properly deal with the dynamics of time-dependent non-Hermitian Hamiltonian. Recently a quantum metric framework has been proposed to study the dynamics of generated defects of a non-Hermitian system under linear quench. Here, we provide an explicit expression for the endowed Hamiltonian under quantum metric for a general two-level non-Hermitian system. Then we propose two exactly solvable models for the study of nonadiabatic dynamics of non-Hermitian systems, and analyze the defect production using the metric method. We find that, in contrast to the direct normalization method, the metric method can reproduce the symmetry of generated defects. The power-law scaling of generated defects with respect to quench time is also obtained.
- quantum metric,
- non-Hermitian,
- quench,
- non-adiabatic

References

Yoshida T, Peters R and Kawakami N 2018 Phys. Rev. B 98 035141

Google Scholar Pub Med

Shen H and Fu L 2018 Phys. Rev. Lett. 121 026403

Google Scholar Pub Med

Nagai Y, Qi Y, Isobe H, Kozii V and Fu L 2020 Phys. Rev. Lett. 125 227204

Google Scholar Pub Med

Makris K G, El-Ganainy R, Christodoulides D N and Musslimani Z H 2008 Phys. Rev. Lett. 100 103904

Google Scholar Pub Med

Klaiman S, Günther U and Moiseyev N 2008 Phys. Rev. Lett. 101 080402

Google Scholar Pub Med

Malzard S, Poli C and Schomerus H 2015 Phys. Rev. Lett. 115 200402

Google Scholar Pub Med

Rotter I 2009 J. Phys. A: Math. Theor. 42 153001

Google Scholar Pub Med

Mao Y, Zhong P, Lin H, Wang X and Hu S 2024 Chin. Phys. Lett. 41 070301

Google Scholar Pub Med

Hodaei H, Hassan A U, Wittek S, Garcia-Gracia H, El-Ganainy R, Christodoulides D N and Khajavikhan M 2017 Nature 548 187

Google Scholar Pub Med

Bergholtz E J, Budich J C and Kunst F K 2021 Rev. Mod. Phys. 93 015005

Google Scholar Pub Med

Zhang S M, He T Y and Jin L 2024 Chin. Phys. Lett. 41 027201

Google Scholar Pub Med

Zhang K, Yang Z and Fang C 2020 Phys. Rev. Lett. 125 126402

Google Scholar Pub Med

Zhang X J, Zhang T, Lu M H and Chen Y F 2022 Adv. Phys. X 7 2109431

Google Scholar Pub Med

Lamata L, León J, Schätz T and Solano E 2007 Phys. Rev. Lett. 98 253005

Google Scholar Pub Med

Liégeois B, Chitra R and Defenu N 2023 Phys. Rev. D 108 116014

Google Scholar Pub Med

Lee T E 2016 Phys. Rev. Lett. 116 133903

Google Scholar Pub Med

Yao S and Wang Z 2018 Phys. Rev. Lett. 121 086803

Google Scholar Pub Med

Song F, Yao S and Wang Z 2019 Phys. Rev. Lett. 123 246801

Google Scholar Pub Med

Kunst F K, Edvardsson E, Budich J C and Bergholtz E J 2018 Phys. Rev. Lett. 121 026808

Google Scholar Pub Med

Xiong Y 2018 J. Phys. Commun. 2 035043

Google Scholar Pub Med

Jin L and Song Z 2019 Phys. Rev. B 99 081103

Google Scholar Pub Med

Borgnia D S, Kruchkov A J and Slager R J 2020 Phys. Rev. Lett. 124 056802

Google Scholar Pub Med

Xu Z and Chen S 2021 Phys. Rev. A 103 043325

Google Scholar Pub Med

Pan L, Chen X, Chen Y and Zhai H 2020 Nat. Phys. 16 767

Google Scholar Pub Med

Lin Z, Zhang L, Long X, Fan Y a, Li Y, Tang K, Li J, Nie X, Xin T, Liu X J et al. 2022 npj Quantum Information 8 77

Google Scholar Pub Med

Liu H, Yang X, Tang K, Che L, Nie X, Xin T, Li J and Lu D 2023 Phys. Rev. A 107 062608

Google Scholar Pub Med

Kawabata K, Numasawa T and Ryu S 2023 Phys. Rev. X 13 021007

Google Scholar Pub Med

Yoshimura T, Bidzhiev K and Saleur H 2020 Phys. Rev. B 102 125124

Google Scholar Pub Med

McDonald A, Hanai R and Clerk A A 2022 Phys. Rev. B 105 064302

Google Scholar Pub Med

Zhai L J, Huang G Y and Yin S 2022 Phys. Rev. B 106 014204

Google Scholar Pub Med

Das Agarwal K, Konar T K, Lakkaraju L G C and Sen (De) A 2024 Phys. Rev. A 110 012226

Google Scholar Pub Med

Das Agarwal K, Konar T K, Lakkaraju L G C and Sen (De) A 2023 arXiv: 2305.08374v1 [quant-ph]

Google Scholar Pub Med

Matsoukas-Roubeas A S, Roccati F, Cornelius J, Xu Z, Chenu A and del Campo A 2023 J. High Energy Phys. 2023 1

Google Scholar Pub Med

Dong X P, Feng Z B, Lu X J, Li M and Zhao Z Y 2023 Chin. Phys. B 32 034201

Google Scholar Pub Med

Ashida Y, Gong Z and Ueda M 2020 Adv. Phys. 69 249

Google Scholar Pub Med

Turkeshi X and Schiró M 2023 Phys. Rev. B 107 L020403

Google Scholar Pub Med

Dóra B, Heyl M and Moessner R 2019 Nat. Commun. 10 2254

Google Scholar Pub Med

Bácsi A and Dóra B 2021 Phys. Rev. B 103 085137

Google Scholar Pub Med

Dóra B, Sticlet D and Moca C P 2022 Phys. Rev. Lett. 128 146804

Google Scholar Pub Med

Dóra B and Moca C P 2020 Phys. Rev. Lett. 124 136802

Google Scholar Pub Med

Longstaff B and Graefe E M 2019 Phys. Rev. A 100 052119

Google Scholar Pub Med

Brody D C 2013 J. Phys. A: Math. Theor. 47 035305

Google Scholar Pub Med

Jing Y, Dong J J, Zhang Y Y and Hu Z X 2024 Phys. Rev. Lett. 132 220402

Google Scholar Pub Med

Mostafazadeh A 2020 Entropy 22 471

Google Scholar Pub Med

Fring A and Moussa M H Y 2016 Phys. Rev. A 93 042114

Google Scholar Pub Med

Mostafazadeh A 2018 Phys. Rev. D 98 046022

Google Scholar Pub Med

Fring A and Moussa M H Y 2016 Phys. Rev. A 93 042114

Google Scholar Pub Med

Fring A and Frith T 2018 J. Phys. A: Math. Theor. 51 265301

Google Scholar Pub Med

Feinberg J and Znojil M 2022 J. Math. Phys. 63 013505

Google Scholar Pub Med

Carmichael H 1993 An Open Systems Approach to Quantum Optics (Berlin: Verlag)

Google Scholar Pub Med

Graefe E M, Korsch H J and Niederle A E 2008 Phys. Rev. Lett. 101 150408

Google Scholar Pub Med

Ashida Y and Ueda M 2018 Phys. Rev. Lett. 120 185301

Google Scholar Pub Med

Sim K, Defenu N, Molignini P and Chitra R 2023 Phys. Rev. Lett. 131 156501

Google Scholar Pub Med

Sim K, Defenu N, Molignini P and Chitra R 2025 Phys. Rev. Res. 7 013325

Google Scholar Pub Med

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Exactly solvable models for non-Hermitian systems under nonadiabatic quench dynamics

Received Date: 30/11/2024
Accepted Date: 22/01/2025

Fund Project:

Key words:

Abstract: Due to the nonunitary time evolution and possibly complex energy eigenvalues in non-Hermitian systems, it is still under debate how to properly deal with the dynamics of time-dependent non-Hermitian Hamiltonian. Recently a quantum metric framework has been proposed to study the dynamics of generated defects of a non-Hermitian system under linear quench. Here, we provide an explicit expression for the endowed Hamiltonian under quantum metric for a general two-level non-Hermitian system. Then we propose two exactly solvable models for the study of nonadiabatic dynamics of non-Hermitian systems, and analyze the defect production using the metric method. We find that, in contrast to the direct normalization method, the metric method can reproduce the symmetry of generated defects. The power-law scaling of generated defects with respect to quench time is also obtained.

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