| Yoshida T, Peters R and Kawakami N 2018 Phys. Rev. B 98 035141 |
| Shen H and Fu L 2018 Phys. Rev. Lett. 121 026403 |
| Nagai Y, Qi Y, Isobe H, Kozii V and Fu L 2020 Phys. Rev. Lett. 125 227204 |
| Makris K G, El-Ganainy R, Christodoulides D N and Musslimani Z H 2008 Phys. Rev. Lett. 100 103904 |
| Klaiman S, Günther U and Moiseyev N 2008 Phys. Rev. Lett. 101 080402 |
| Malzard S, Poli C and Schomerus H 2015 Phys. Rev. Lett. 115 200402 |
| Rotter I 2009 J. Phys. A: Math. Theor. 42 153001 |
| Mao Y, Zhong P, Lin H, Wang X and Hu S 2024 Chin. Phys. Lett. 41 070301 |
| Hodaei H, Hassan A U, Wittek S, Garcia-Gracia H, El-Ganainy R, Christodoulides D N and Khajavikhan M 2017 Nature 548 187 |
| Bergholtz E J, Budich J C and Kunst F K 2021 Rev. Mod. Phys. 93 015005 |
| Zhang S M, He T Y and Jin L 2024 Chin. Phys. Lett. 41 027201 |
| Zhang K, Yang Z and Fang C 2020 Phys. Rev. Lett. 125 126402 |
| Zhang X J, Zhang T, Lu M H and Chen Y F 2022 Adv. Phys. X 7 2109431 |
| Lamata L, León J, Schätz T and Solano E 2007 Phys. Rev. Lett. 98 253005 |
| Liégeois B, Chitra R and Defenu N 2023 Phys. Rev. D 108 116014 |
| Lee T E 2016 Phys. Rev. Lett. 116 133903 |
| Yao S and Wang Z 2018 Phys. Rev. Lett. 121 086803 |
| Song F, Yao S and Wang Z 2019 Phys. Rev. Lett. 123 246801 |
| Kunst F K, Edvardsson E, Budich J C and Bergholtz E J 2018 Phys. Rev. Lett. 121 026808 |
| Xiong Y 2018 J. Phys. Commun. 2 035043 |
| Jin L and Song Z 2019 Phys. Rev. B 99 081103 |
| Borgnia D S, Kruchkov A J and Slager R J 2020 Phys. Rev. Lett. 124 056802 |
| Xu Z and Chen S 2021 Phys. Rev. A 103 043325 |
| Pan L, Chen X, Chen Y and Zhai H 2020 Nat. Phys. 16 767 |
| 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 |
| Liu H, Yang X, Tang K, Che L, Nie X, Xin T, Li J and Lu D 2023 Phys. Rev. A 107 062608 |
| Kawabata K, Numasawa T and Ryu S 2023 Phys. Rev. X 13 021007 |
| Yoshimura T, Bidzhiev K and Saleur H 2020 Phys. Rev. B 102 125124 |
| McDonald A, Hanai R and Clerk A A 2022 Phys. Rev. B 105 064302 |
| Zhai L J, Huang G Y and Yin S 2022 Phys. Rev. B 106 014204 |
| Das Agarwal K, Konar T K, Lakkaraju L G C and Sen (De) A 2024 Phys. Rev. A 110 012226 |
| Das Agarwal K, Konar T K, Lakkaraju L G C and Sen (De) A 2023 arXiv: 2305.08374v1 [quant-ph] |
| Matsoukas-Roubeas A S, Roccati F, Cornelius J, Xu Z, Chenu A and del Campo A 2023 J. High Energy Phys. 2023 1 |
| Dong X P, Feng Z B, Lu X J, Li M and Zhao Z Y 2023 Chin. Phys. B 32 034201 |
| Ashida Y, Gong Z and Ueda M 2020 Adv. Phys. 69 249 |
| Turkeshi X and Schiró M 2023 Phys. Rev. B 107 L020403 |
| Dóra B, Heyl M and Moessner R 2019 Nat. Commun. 10 2254 |
| Bácsi A and Dóra B 2021 Phys. Rev. B 103 085137 |
| Dóra B, Sticlet D and Moca C P 2022 Phys. Rev. Lett. 128 146804 |
| Dóra B and Moca C P 2020 Phys. Rev. Lett. 124 136802 |
| Longstaff B and Graefe E M 2019 Phys. Rev. A 100 052119 |
| Brody D C 2013 J. Phys. A: Math. Theor. 47 035305 |
| Jing Y, Dong J J, Zhang Y Y and Hu Z X 2024 Phys. Rev. Lett. 132 220402 |
| Mostafazadeh A 2020 Entropy 22 471 |
| Fring A and Moussa M H Y 2016 Phys. Rev. A 93 042114 |
| Mostafazadeh A 2018 Phys. Rev. D 98 046022 |
| Fring A and Moussa M H Y 2016 Phys. Rev. A 93 042114 |
| Fring A and Frith T 2018 J. Phys. A: Math. Theor. 51 265301 |
| Feinberg J and Znojil M 2022 J. Math. Phys. 63 013505 |
| Carmichael H 1993 An Open Systems Approach to Quantum Optics (Berlin: Verlag) |
| Graefe E M, Korsch H J and Niederle A E 2008 Phys. Rev. Lett. 101 150408 |
| Ashida Y and Ueda M 2018 Phys. Rev. Lett. 120 185301 |
| Sim K, Defenu N, Molignini P and Chitra R 2023 Phys. Rev. Lett. 131 156501 |
| Sim K, Defenu N, Molignini P and Chitra R 2025 Phys. Rev. Res. 7 013325 |