[1] Hasan M Z, Kane C L[J]. Rev. Mod. Phys., 82, 3045(2010).

[2] Qi X L, Zhang S C[J]. Rev. Mod. Phys., 83, 1057(2011).

[3] Jotzu G, Messer M, Desbuquois R, Lebrat M, Uehlinger T, Greif D, Esslinger T[J]. Nature, 515, 237(2014).

[4] Fläschner N, Rem B S, Tarnowski M, Vogel D, Lühmann D S, Sengstock K, Weitenberg C[J]. Science, 352, 1091(2016).

[5] Wu Z, Zhang L, Sun W, Xu X T, Wang B Z, Ji S C, Deng Y, Chen S, Liu X J, Pan J W[J]. Science, 354, 83(2016).

[6] Song B, Zhang L, He C, Poon T F J, Haiiyev E, Zhang S, Liu X J, Jo G B[J]. Sci. Adv., 4, 4748(2018).

[7] Poli C, Bellec M, Kuhl U, Mortessagne F, Schomerus H[J]. Nat. Commun., 6, 6710(2015).

[8] Weimann S, Kremer M, Plotnik Y, Lumer Y, Nolte S, Makris K G, Segev M, Rechtsman M C, Szameit A[J]. Nat. Mater., 16, 433(2017).

[9] Xiao L, Zhan X, Bian Z H, Wang K K, Zhang X, Wang X P, Li J, Mochizuki K, Kim D, Kawakami N, Yi W, Obuse H, Sanders B C, Xue P[J]. Nat. Phys., 13, 1117(2017).

[10] Zeuner J M, Rechtsman M C, Plotnik Y, Lumer Y, Nolte S, Rudner M S, Segev M, Szameit A[J]. Phys. Rev. Lett., 115, 040402(2015).

[11] Zhan X, Xiao L, Bian Z, Wang K, Qiu X, Sanders B C, Yi W, Xue P[J]. Phys. Rev. Lett., 119, 130501(2017).

[12] Shen H, Zhen B, Fu L[J]. Phys. Rev. Lett., 120, 146402(2018).

[13] Chen Y, Zhai H[J]. Phys. Rev. B, 98, 245130(2018).

[14] Kunst F K, Edvardsson E, Budich J C, Bergholtz E J[J]. Phys. Rev. Lett., 121, 026808(2018).

[15] Yao S, Wang Z[J]. Phys. Rev. Lett., 121, 086803(2018).

[16] Yao S, Song F, Wang Z[J]. Phys. Rev. Lett., 121, 136802(2018).

[17] Caio M D, Cooper N R, Bhaseen M J[J]. Phys. Rev. Lett., 115, 236403(2015).

[18] D’Alessio L, Rigol M[J]. Nat. Commun., 6, 8336(2015).

[19] Wang C, Zhang P, Chen X, Yu J, Zhai H[J]. Phys. Rev. Lett., 118, 185701(2017).

[20] Yang C, Li L, Chen S[J]. Phys. Rev. B, 97, 060304(2018).

[21] Gong Z, Ueda M[J]. Phys. Rev. Lett., 121, 250601(2018).

[22] Zhang L, Zhang L, Niu S, Liu X J[J]. Science Bulletin, 63, 1385(2018).

[23] Zhang L, Zhang L, Liu X J[J]. arXiv: 1807.10782 condmat.quant-gas(2018).

[24] Fläschner N, Vogel D, Tarnowski M, Rem B S, Lühmann D S, Heyl M, Budich J C, Mathey L, Sengstock K, Weitenberg C[J]. Nat. Phys., 14, 265(2018).

[25] Tarnowski M, Nur-Unal F, Flaschner N, Rem B S, Eckard A, Sengstock K, Weitenberg C[J]. arXiv:1709.01046 condmat.quant-gas(2017).

[26] Sun W, Yi C R, Wang B Z, Zhang W W, Sanders B C, XuX T, Wang Z Y, Schmiedmayer J, Deng Y J, Liu X J, ChenS , Pan J W[J]. Phys. Rev. Lett., 121, 250403(2018).

[27] Guo X Y, Yang C, Zeng Y, Peng Y, Li H K, Deng H, Jin YR, Chen S, Zheng D N, Fan H[J]. arXiv:1806.09269 condmat.stat-mech(2018).

[28] Wang K, Qiu X, Xiao L, Zhan X, Bina Z, Yi W, Xue P[J]. Phys. Rev. Lett., 122, 020501(2019).

[29] Tian T, Ke K, Zhang L, Lin L, Shi Z, Huang P, Lee C, Du J[J]. arXiv:1807.04483 quant-ph(2018).

[30] Xu X Y, Wang Q Q, Heyl M, Budich J C, Pan W W, Chen Z, Jan M, Sun K, Xu J S, Han Y J, Li C F, Guo G C[J]. arXiv:1808.03930 quant-ph(2018).

[31] Wang K, Qiu X, Xiao L, Zhan X, Bian Z, Yi W, Xue P[J]. arXiv:1808.06446 quant-ph(2018).

[32] Heyl M, Polkovnikov A, Kehrein S[J]. Phys. Rev. Lett., 110, 135704(2013).

[33] Heyl M[J]. Phys. Rev. Lett., 115, 140602(2015).

[34] Heyl M[J]. Rep. Prog. Phys., 81, 054001(2018).

[35] Budich J C, Heyl M[J]. Phys. Rev. B, 93, 085416(2016).

[36] Huang Z, Balatsky A V[J]. Phys. Rev. Lett., 117, 086802(2016).

[37] Vajna S, Dora B[J]. Phys. Rev. B, 91, 155127(2015).

[38] Zhou L W, Wang Q H, Wang H L[J]. Phys. Rev. A, 98, 022129(2018).

[39] Gu J, Sun K[J]. Phys. Rev. B, 94, 12511(2016).

[40] Qiu X, Deng T S, Guo G C, Yi W[J]. Phys. Rev. A, 98, 021601(2018).

[41] Qiu X, Deng T S, Hu Y, Xue P, Yi W[J]. arXiv:1806.10268 cond-mat.quant-gas(2018).

[42] Bender C M, Boettcher S[J]. Phys. Rev. Lett., 80, 5243(1998).

[43] Bender C M, Brody D C, Jones H F[J]. Phys. Rev. Lett., 89, 270401(2002).

[44] Bender C M[J]. Rep. Prog. Phys., 70, 947(2007).

[45] Su W P, Schrieffer J R, Heeger A J[J]. Phys. Rev. Lett., 42, 1698(1979).

[46] Zhu B, Lu R, Chen S[J]. Phys. Rev. A, 89, 062102(2014).

[47] Garrison J, Wright E[J]. Phys. Lett. A, 128, 177(1988).

[48] Brody D C[J]. J. Phys. A: Math. Theor., 47, 035305(2014).

[49] Li J, Harter A K, Liu J, de Melo L, Joglekar Y N, Luo L[J]. arXiv:1608.05061 cond-mat.quant-gas(2016).

[50] Kohei K, Yuto A, Hosho K, Masahito U[J]. Phys. Rev. B, 98, 085116(2018).