Symmetries and effect of time dimension in non-equilibrium quantum matter

Cai Zi

doi:10.7498/aps.70.20211741

Abstract

Non-equilibrium quantum many-body systems have attracted considerable attention in the past decades. The scope of the research of this kind of novel system involves interdisciplinary research of condensed matter, atomic and molecular physics, quantum optics, quantum information and quantum computation, as well as the non-equilibrium statistical physics. The non-equilibrium phenomena emerging from the aforementioned quantum systems can exhibit rich and universal behaviors, which have far from being well understood due to the novelties and complexities of these systems, and hence the quantum many-body physics becomes the research highlight. At the same time, with the rapid development of quantum techniques, the understanding of these complex systems is of important practical significance due to their potential applications in quantum computation and quantum manipulation. In this paper, we show our recent progress of non-equilibrium quantum many-body systems. We focus on the novel phenomena closely related to the temporary symmetry breaking, including the exotic quantum matter, quasi-particles as well as the dynamical universality classes in non-equilibrium quantum many-body systems.

Keywords:

Authors and contacts

Cai Zi

School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China

Corresponding author: Cai Zi, zcai@sjtu.edu.cn

Funds: Project supported by the National Key Research and Development Program of China (Grant No. 2020YFA0309000), the National Natural Science Foundation of China (Grant No. 12174251), and the Shanghai Municipal Science and Technology Major Project, China (Grant No. 2019SHZDZX01).

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References

[1]	张广铭, 于渌 2010 物理 39 543 Zhang G M, Yu L 2010 Physics 39 543
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[35]	McGinley M, Cooper N R 2020 Nat. Phys. 16 1181 Google Scholar
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Cited By

图 1 (a) 分立时间晶体态的示意图; (b) 通过含时扰动局部破坏周期驱动的周期性, 导致时间晶体瞬子激发(不同简并时间晶体之间的隧穿)

Figure 1. Schematic diagram of (a) a period doubling dynamics in the presence of periodical driving and two degenerate TC phases and (b) the phase ramping protocol in our model and an instanton-like excitation induced by it.

DownLoad: Full-Size Img PowerPoint

图 2 (a)虚时间晶体在2+1维欧几里得时空中一种典型的时空构型的示意图; (b) 其物理性质随温度振荡

Figure 2. (a) A typical world-line configurations of iTC in a (2+1)D Euclidean space; (b) the (inverse) temperature dependence of the CDW order parameter in the iTC phase.

DownLoad: Full-Size Img PowerPoint

图 4 量子多体系统在无序、噪声、相互作用、对称性等因素共同作用下产生普适的弛豫动力学行为

Figure 4. Schematic of a open quantum many-body system and its universal dynamics induced by the interplay between disorder, noise, interaction and symmetry.

DownLoad: Full-Size Img PowerPoint

图 3 一条对称保护的拓扑量子态(AKLT态)通过不同的方式, 耦合上不同量子环境的示意图

Figure 3. Schematic of the symmetry-protected topological systems (AKLT state) coupled to different quantum baths via various SB couplings.

DownLoad: Full-Size Img PowerPoint

图 5 耗散-驱动玻色-赫伯特模型的非平衡稳态中涌现的条纹相 (a), (b) 和奇异玻色液体态(c), (d)

Figure 5. The stripe phase (a), (b) and the exotic bose liquid (c), (d) emerging from the steady state of a dissipative-driven Bose Hubbard model.

DownLoad: Full-Size Img PowerPoint

图 6 当前处理非平衡量子关联系统的部分解析与数值方法

Figure 6. A review of current analytical and numerical methods to deal with non-equilibrium quantum many-body systems.

DownLoad: Full-Size Img PowerPoint

[1]	张广铭, 于渌 2010 物理 39 543 Zhang G M, Yu L 2010 Physics 39 543
[2]	Fausti D, Tobey R I, Dean N, Kasier S, Dienst A, Hoffmann M C, Pyon S, Takayama T, Takagi H, Cavalleri A 2011 Science 331 189 Google Scholar
[3]	Wan Y, Moessner R 2017 Phys. Rev. Lett. 119 167203 Google Scholar
[4]	Lindner N H, Refael G, Galitski V 2011 Nat. Phys. 7 490 Google Scholar
[5]	Wang Y H, Steinberg H, Jarillo-Herrero P, Gedik N 2013 Science 342 453 Google Scholar
[6]	Wilczek F 2012 Phys. Rev. Lett. 109 160401 Google Scholar
[7]	Mankowsky R, Subedi A, Forst M, Mariager S O, Chollet M, Lemke H T, Robinson J S, Glownia J M, Minitti M P, Frano A, Fechner M, Spaldin N A, Loew T, Keimer B, Georges A, Cavalleri A 2014 Nature 516 71 Google Scholar
[8]	Kuehn W, Reimann K, Woerner M, Elsaesser T, Hey R 2011 J. Phys. Chem. B 115 5448 Google Scholar
[9]	Yang Y, Tang T, Duan S, Zhou C, Hao D, Zhang W 2019 Rev. Sci. Instrum. 90 063905 Google Scholar
[10]	Rigol M, Dunjko V, Olshanii M 2008 Nature (London) 452 854
[11]	Polkovnikov A, Sengupta K, Silva A, Vengalattore M 2011 Rev. Mod. Phys. 83 863 Google Scholar
[12]	Gring M, Kuhnert M, Langen T, Kitagawa T, Rauer B, Schreitl M, Mazets I, Smith D A, Demler E, Schmiedmayer J 2012 Science 337 1318 Google Scholar
[13]	Trotzky S, Chen Y A, Flesch A, McCulloch I P, Schollwöck U, Eisert J, Bloch I 2012 Nat. Phys. 8 325 Google Scholar
[14]	Braun S, Friesdorf M, Hodgman S S, Schreiber M, Ronzheimer J P, Riera A, del Rey M, Bloch I, Eisert J, Schneider U 2015 Proc. Natl. Acad. Sci. 112 3641 Google Scholar
[15]	Clark L W, Feng L, Chin C 2016 Science 354 606 Google Scholar
[16]	Struck J, Ölschläger C, Le Targat R, Soltan-Panahi P, Eckardt A, Lewenstein M, Windpassinger P, Sengstock K 2011 Science 333 996 Google Scholar
[17]	Struck J, Ölschläger C, Weinberg M, Hauke P, Simonet J, Eckardt A, Lewenstein M, Sengstock K, Windpassinger P 2012 Phys. Rev. Lett. 108 225304 Google Scholar
[18]	Jotzu G, Messer M, Desbuquois R, Lebrat M, Uehlinger T, Greif D, Esslinger T 2014 Nature 515 237 Google Scholar
[19]	Clark L W, Anderson B M, Feng L, Gaj A, Levin K, Chin C, 2018 Phys. Rev. Lett. 121 030402 Google Scholar
[20]	Yang X, Cai Z 2021 Phys. Rev. Lett. 126 020602 Google Scholar
[21]	Cai Z, Huang Y, Liu W V 2020 Chin. Phys. Lett. 37 050503 Google Scholar
[22]	Wang Z J, Li Q Y, Li W, Cai Z 2021 Phys. Rev. Lett. 126 237201 Google Scholar
[23]	Ren J, Li Q Y, Li W, Cai Z, Wang X Q 2020 Phys. Rev. Lett. 124 130602 Google Scholar
[24]	Wang Z J, Navarrete-Benlloch C, Cai Z 2020 Phys. Rev. Lett. 125 115301 Google Scholar
[25]	Watanabe H, Oshikawa M 2015 Phys. Rev. Lett. 114 251603 Google Scholar
[26]	Else D V, Bauer B, Nayak C 2016 Phys. Rev. Lett. 117 090402 Google Scholar
[27]	Khemani V, Lazarides A, Moessner R, Sondhi S 2016 Phys. Rev. Lett. 116 250401 Google Scholar
[28]	Choi S, Choi J, Landig R, Kucsko G, Zhou H Y, Isoya J C, Jelezko F, Onoda S, Sumiya H, Khemani V, von Keyserlingk C, Yao N Y, Demler E, Lukin M D 2017 Nature 543 221 Google Scholar
[29]	Zhang J, Hess P W, Kyprianidis A, Becker P, Lee A, Smith J, Pagano G, Potirniche I Q, Potter A C, Vishwanath A, Yao N Y, Monroe C 2017 Nature 543 217 Google Scholar
[30]	Su W P, Schrieffer J R, Heeger A J 1979 Phys. Rev. Lett. 42 1698 Google Scholar
[31]	Kozii V, Fu L 2017 arXiv: 1708.05841
[32]	Nayak C, Simon S H, Stern A, Freedman M, Das Sarma S 2008 Rev. Mod. Phys. 80 1083 Google Scholar
[33]	Chen X, Gu Z C, Liu Z X, Wen X G 2012 Science 338 1604 Google Scholar
[34]	Kane C L, Mele E J 2005 Phys. Rev. Lett. 95 146802 Google Scholar
[35]	McGinley M, Cooper N R 2020 Nat. Phys. 16 1181 Google Scholar
[36]	Affleck I, Kennedy T, Lieb E H, Tasaki H 1987 Phys. Rev. Lett. 59 799 Google Scholar
[37]	Berg E, Torre E G D, Giamarchi T, Altman E 2009 Phys. Rev. B 77 245119
[38]	Deng T S, Pan L, Chen Y, Zhai H 2021 Phys. Rev. Lett. 127 086801 Google Scholar
[39]	Hohenberg P C, Halperin B I 1977 Rev. Mod. Phys. 49 435 Google Scholar
[40]	Kardar M, Parisi G, Zhang Y C 1986 Phys. Rev. Lett. 56 889 Google Scholar
[41]	Lüschen H P, Bordia P, Hodgman S S, Schreiber M, Sarkar S, Daley A J, Fischer M H, Altman E, Bloch I, Schneider U 2017 Phys. Rev. X 7 011034
[42]	Bouganne R, Aguilera M B, Ghermaoui A, Beugnon J, Gerbier F 2020 Nat. Phys. 16 21
[43]	Cross M Greenside H 2009 Pattern Formation and Dynamics in Nonequilibrium Systems (Cambridge: Cambridge University Press)
[44]	Pethick C J, Smith H 2002 Bose–Einstein Condensation in Dilute Gases (Cambridge: Cambridge University Press)
[45]	Daley A J, Kollath C, Schollwöck U, Vidal G 2005 J. Stat. Mech. P04005
[46]	Mitra A, Giamarchi T 2012 Phys. Rev. B 85 075117 Google Scholar
[47]	Kamenev A 2011 Field Theory of Non-equilibrium Systems (Cambridge: Cambridge University Press)
[48]	Cai Z, Schollwock U, Pollet L 2014 Phys. Rev. Lett. 113 260403 Google Scholar
[49]	Aoki H, Tsuji N, Eckstein M, Kollar M, Oka T, Werner P 2014 Rev. Mod. Phys. 86 779 Google Scholar

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