[1] Breuer H P and Petruccione F 2002 The Theory of Open Quantum Systems (Oxford: Oxford University Press) [2] Xu Y, Wang S T and Duan L M 2017 Phys. Rev. Lett. 118 045701 [3] Gong Z, Ashida Y, Kawabata K, Takasan K, Higashikawa S and Ueda M 2018 Phys. Rev. X 8 031079 [4] Kunst F K, Edvardsson E, Budich J C and Bergholtz E J 2018 Phys. Rev. Lett. 121 026808 [5] Yao S and Wang Z 2018 Phys. Rev. Lett. 121 086803 [6] Lee C H and Thomale R 2019 Phys. Rev. B 99 201103 [7] Kawabata K, Shiozaki K, Ueda M and Sato M 2019 Phys. Rev. X 9 041015 [8] Xiao L, Deng T, Wang K, Zhu G, Wang Z, Yi W and Xue P 2019 Nat. Phys. 16 761 [9] Helbig T, Hofmann T, Imhof S, Abdelghany M, Kieβling T, Molenkamp L W, Lee C H, Szameit A, Greiter M and Thomale R 2020 Nat. Phys. 16 747 [10] Borgnia D, Kruchkov A J and Slager R J 2020 Phys. Rev. Lett. 124 056802 [11] Okuma N, Kawabata K, Shiozaki K and Sato M 2020 Phys. Rev. Lett. 124 086801 [12] Weidemann S, Kremer M, Helbig T, Hofmann T, Stegmaier A, Greiter M, Thomale R and Szameit A 2020 Science 368 eaaz8727 [13] Longhi S 2020 Phys. Rev. Lett. 124 066602 [14] Bergholtz E J, Budich J C and Kunst F K 2021 Rev. Mod. Phys. 93 015005 [15] Wang K, Dutt A, Yang K Y, Wojcik C C, Vučković J and Fan S 2021 Science 371 1240 [16] Wang K, Li T, Xiao L, Han Y, Yi W and Xue P 2021 Phys. Rev. Lett. 127 270602 [17] Hatano N and Nelson D R 1996 Phys. Rev. Lett. 77 570 [18] Hatano N and Nelson D R 1998 Phys. Rev. B 58 8384 [19] Abrahams E, Anderson P W, Licciardello D C and Ramakrishnan T V 1979 Phys. Rev. Lett. 42 673 [20] Lee P A and Ramakrishnan T V 1985 Rev. Mod. Phys. 57 287 [21] Evers F and Mirlin A D 2008 Rev. Mod. Phys. 80 1355 [22] Tzortzakakis A F, Makris K G and Economou E N 2020 Phys. Rev. B 101 014202 [23] Huang Y and Shklovskii B I 2020 Phys. Rev. B 101 014204 [24] Jazaeri A and Satija I I 2001 Phys. Rev. E 63 036222 [25] Yuce C 2014 Phys. Lett. A 378 2024 [26] Zeng Q B, Chen S and Lü R 2017 Phys. Rev. A 95 062118 [27] Jiang H, Lang L J, Yang C, Zhu S L and Chen S 2019 Phys. Rev. B 100 054301 [28] Longhi S 2019 Phys. Rev. B 100 125157 [29] Longhi S 2019 Phys. Rev. Lett. 122 237601 [30] Zeng Q B, Yang Y B and Xu Y 2020 Phys. Rev. B 101 020201 [31] Liu Y, Jiang X P, Cao J and Chen S 2020 Phys. Rev. B 101 174205 [32] Zeng Q B and Xu Y 2020 Phys. Rev. Res. 2 033052 [33] Liu T, Guo H, Pu Y and Longhi S 2020 Phys. Rev. B 102 024205 [34] Liu Y, Wang Y, Zheng Z and Chen S 2021 Phys. Rev. B 103 134208 [35] Liu Y, Zhou Q and Chen S 2021 Phys. Rev. B 104 024201 [36] Wang Y, Xia X, Wang Y, Zheng Z and Liu X J 2021 Phys. Rev. B 103 174205 [37] Cai X 2021 Phys. Rev. B 103 014201 [38] Gong L Y, Lu H and Cheng W W 2021 Advanced Theory and Simulations 4 2100135 [39] Liu Y, Wang Y, Liu X J, Zhou Q and Chen S 2021 Phys. Rev. B 103 014203 [40] Dwiputra D and Zen F P 2022 Phys. Rev. B 105 L081110 [41] Aubry S and André G 1980 Proceedings, VIII International Colloquium on Group-Theoretical Methods in Physics 3 [42] Biddle J and Sarma S D 2010 Phys. Rev. Lett. 104 070601 [43] Deng X, Ray S, Sinha S, Shlyapnikov G V and Santos L 2019 Phys. Rev. Lett. 123 025301 [44] Yao H, Khoudli H, Bresque L and Sanchez-Palencia L 2019 Phys. Rev. Lett. 123 070405 [45] Wang Y, Xia X, Zhang L, Yao H, Chen S, You J, Zhou Q and Liu X J 2020 Phys. Rev. Lett. 125 196604 [46] Roy S, Mishra T, Tanatar B and Basu S 2021 Phys. Rev. Lett. 126 106803 [47] Liu T, Xia X, Longhi S and Sanchez-Palencia L 2022 SciPost Phys. 12 027 [48] Avila A 2015 Acta Mathematica 215 1 [49] Lüschen H P, Scherg S, Kohlert T, Schreiber M, Bordia P, Li X, Das Sarma S and Bloch I 2018 Phys. Rev. Lett. 120 160404 [50] An F A, Padavić K, Meier E J, Hegde S, Ganeshan S, Pixley J H, Vishveshwara S and Gadway B 2021 Phys. Rev. Lett. 126 040603 [51] Wang Y, Zhang J H, Li Y, Wu J, Liu W, Mei F, Hu Y, Xiao L, Ma J, Chin C and Jia S 2022 Phys. Rev. Lett. 129 103401 [52] Lin Q, Li T, Xiao L, Wang K, Yi W and Xue P 2022 Phys. Rev. Lett. 129 113601 [53] Luo X, Ohtsuki T and Shindou R 2021 Phys. Rev. Lett. 126 090402 [54] Goblot V, Štrkalj A, Pernet N, Lado J L, Dorow C, Lemaître A, Le Gratiet L, Harouri A, Sagnes I, Ravets S, Amo A, Bloch J and Zilberberg O 2020 Nat. Phys. 16 832 [55] Rousha P, Neill C, Tangpanitanon J, Bastidas V M, Megrant A, Barends R, Chen Y, Chen Z, Chiaro B, Dunsworth A, Fowler A, Foxen B, Giustina M, Jeffrey E, Kelly J, Lucero E, Mutus J, Neeley M, Quintana C, Sank D, Vainsencher A, Wenner J, White T, Neven H, Angelakis D G and Martinis J 2017 Science 358 1175 [56] Lahini Y, Pugatch R, Pozzi F, Sorel M, Morandotti R, Davidson N and Silberberg Y 2009 Phys. Rev. Lett. 103 013901 [57] Ganeshan S, Pixley J H and Das Sarma S 2015 Phys. Rev. Lett. 114 146601 [58] Liu Y 2022 A general approach to the exact localized transition points of 1d mosaic disorder models (Preprint 2208.02762) [59] Wang Y, Zhang L, Wan Y, He Y and Wang Y 2022 Phys. Rev. B 107 L140201 [60] We use the notion "Lyapunov exponent" because in Hermitian disorder or quasiperiodic systems Lyapunov exponent is just the inverse of the localization length,ucite[64] but how to calculate Lyapunov exponent for nonreciprocal systems using transfer matrix is still an open question. [61] Jitomirskaya S Y 1999 Annals of Mathematics 150 1159 [62] Avila A, You J and Zhou Q 2017 Duke Mathematical Journal 166 2697 [63] Johnson R A 1986 Journal of Differential Equations 61 54 [64] Carmona R 1982 Duke Math. J. 49 191 |