Chin. Phys. Lett.  2022, Vol. 39 Issue (5): 057101    DOI: 10.1088/0256-307X/39/5/057101
CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES |
Quantum Hydrodynamics of Fractonic Superfluids with Lineon Condensate: From Navier–Stokes-Like Equations to Landau-Like Criterion
Jian-Keng Yuan1, Shuai A. Chen2*, and Peng Ye1*
1School of Physics, State Key Laboratory of Optoelectronic Materials and Technologies, and Guangdong Provincial Key Laboratory of Magnetoelectric Physics and Devices, Sun Yat-sen University, Guangzhou 510275, China
2Department of Physics, The Hong Kong University of Science and Technology, Hong Kong, China
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Jian-Keng Yuan, Shuai A. Chen, and Peng Ye 2022 Chin. Phys. Lett. 39 057101
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Abstract Fractonic superfluids are exotic states of matter with spontaneously broken higher-rank $U(1)$ symmetry. The broken symmetry is associated with conserved quantities, including not only particle number (i.e., charge) but also higher moments, such as dipoles, quadrupoles, and angular moments. Owing to the presence of such conserved quantities, the mobility of particles is restricted either completely or partially. Here, we systematically study the hydrodynamical properties of fractonic superfluids, especially focusing on the fractonic superfluids with conserved angular moments. The constituent bosons are called “lineons” with $d$ components in $d$-dimensional space. From the Euler–Lagrange equation, we derive the continuity equation and Navier–Stokes-like equations, in which the angular moment conservation introduces extra terms. Further, we discuss the current configurations related to the defects. Like the conventional superfluid, we study the critical values of velocity fields and density currents, which gives rise to a Landau-like criterion. Finally, several future directions are discussed.
Received: 04 March 2022      Editors' Suggestion Published: 26 April 2022
PACS:  71.27.+a (Strongly correlated electron systems; heavy fermions)  
  47.37.+q (Hydrodynamic aspects of superfluidity; quantum fluids)  
  11.30.-j (Symmetry and conservation laws)  
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https://cpl.iphy.ac.cn/10.1088/0256-307X/39/5/057101       OR      https://cpl.iphy.ac.cn/Y2022/V39/I5/057101
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Jian-Keng Yuan
Shuai A. Chen
and Peng Ye
[1] Yuan J K, Chen S A, and Ye P 2020 Phys. Rev. Res. 2 023267
[2] Chen S A, Yuan J K, and Ye P 2021 Phys. Rev. Res. 3 013226
[3] Li H and Ye P 2021 Phys. Rev. Res. 3 043176
[4] Yuan J K, Chen S A, and Ye P 2022 arXiv:2201.08597 [cond-mat.str-el]
[5] Nandkishore R M and Hermele M 2019 Annu. Rev. Condens. Matter Phys. 10 295
[6] Pretko M, Chen X, and You Y 2020 Int. J. Mod. Phys. A 35 2030003
[7] Chamon C 2005 Phys. Rev. Lett. 94 040402
[8] Haah J 2011 Phys. Rev. A 83 042330
[9] Yoshida B 2013 Phys. Rev. B 88 125122
[10] Vijay S, Haah J, and Fu L 2016 Phys. Rev. B 94 235157
[11] Ma H, Lake E, Chen X, and Hermele M 2017 Phys. Rev. B 95 245126
[12] Vijay S 2017 arXiv:1701.00762 [cond-mat.str-el]
[13] Shirley W, Slagle K, Wang Z, and Chen X 2018 Phys. Rev. X 8 031051
[14] Ma X, Shirley W, Cheng M, Levin M, McGreevy J, and Chen X 2020 arXiv:2010.08917 [cond-mat.str-el]
[15] Aasen D, Bulmash D, Prem A, Slagle K, and Williamson D J 2020 Phys. Rev. Res. 2 043165
[16] Slagle K 2021 Phys. Rev. Lett. 126 101603
[17] Li M Y and Ye P 2020 Phys. Rev. B 101 245134
[18] Li M Y and Ye P 2021 Phys. Rev. B 104 235127
[19] Xu C and Wu C 2008 Phys. Rev. B 77 134449
[20] Pretko M 2017 Phys. Rev. B 95 115139
[21] Ma H, Hermele M, and Chen X 2018 Phys. Rev. B 98 035111
[22] Bulmash D and Barkeshli M 2018 Phys. Rev. B 97 235112
[23] Seiberg N and Shao S H 2021 SciPost Phys. 10 3
[24] Pretko M 2018 Phys. Rev. B 98 115134
[25] Gromov A 2019 Phys. Rev. X 9 031035
[26] Seiberg N 2020 SciPost Phys. 8 050
[27] Zhu G Y, Chen J Y, Ye P, and Trebst S 2022 arXiv:2203.00015 [cond-mat.str-el]
[28] Stahl C, Lake E, and Nandkishore R 2021 arXiv:2111.08041 [cond-mat.stat-mech]
[29] Gorantla P, Lam H T, Seiberg N, and Shao S H 2022 arXiv:2201.10589 [cond-mat.str-el]
[30] Argurio R, Hoyos C, Musso D, and Naegels D 2021 Phys. Rev. D 104 105001
[31] Bidussi L, Hartong J, Have E, Musaeus J, and Prohazka S 2021 arXiv:2111.03668 [hep-th]
[32] Jain A and Jensen K 2021 arXiv:2111.03973 [hep-th]
[33] Angus S, Kim M, and Park J H 2021 arXiv:2111.07947 [hep-th]
[34] Grosvenor K T, Hoyos C, Pe N B F, and Surówka P 2021 arXiv:2112.00531 [hep-th]
[35] Banerjee R 2022 arXiv:2202.00326 [hep-th]
[36] Rogel-Salazar J 2013 Eur. J. Phys. 34 247
[37] Lapa M F, Jian C M, Ye P, and Hughes T L 2017 Phys. Rev. B 95 035149
[38] Han B, Wang H, and Ye P 2019 Phys. Rev. B 99 205120
[39] Ye P and Wen X G 2014 Phys. Rev. B 89 045127
[40] Ye P and Wen X G 2013 Phys. Rev. B 87 195128
[41] Ye P, Hughes T L, Maciejko J, and Fradkin E 2016 Phys. Rev. B 94 115104
[42] Ashida Y, Gong Z, and Ueda M 2020 Adv. Phys. 69 249
[43] Chen L M, Chen S A, and Ye P 2021 SciPost Phys. 11 3
[44] Lee C H, Ye P, and Qi X L 2014 J. Stat. Mech.: Theory Exp. 2014 P10023
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