Express Letter

Imaginary Time Crystal of Thermal Quantum Matter

Funds: Supported in part by the National Key Research and Development Program of China (Grant No. 2016YFA0302001), the National Natural Science Foundation of China (Grant Nos. 11674221 and 11745006), the Shanghai Rising-Star Program, Eastern Scholar Professor of Distinguished Appointment Program, the AFOSR (Grant No. FA9550-16-1-0006), the MURI-ARO (Grant No. W911NF-17-1-0323) through UC Santa Barbara, the NSF China Overseas Scholar Collaborative Program (Grant No. 11429402), and the Shanghai Municipal Science and Technology Major Project (Grant No. 2019SHZDZX01).
  • Received Date: April 07, 2020
  • Published Date: April 30, 2020
  • Temperature is a fundamental thermodynamic variable for matter. Physical observables are often found to either increase or decrease with it, or show a non-monotonic dependence with peaks signaling underlying phase transitions or anomalies. Statistical field theory has established connection between temperature and time: a quantum ensemble with inverse temperature β is formally equivalent to a dynamic system evolving along an imaginary time from 0 to iβ in the space one dimension higher. Here we report that a gas of hard-core bosons interacting with a thermal bath manifests an unexpected temperature-periodic oscillation of its macroscopic observables, arising from the microscopic origin of space-time locked translational symmetry breaking and crystalline ordering. Such a temperature crystal, supported by quantum Monte Carlo simulation, generalizes the concept of purely spatial density-wave order to the imaginary time axis for Euclidean action.
  • Article Text

  • [1]
    Wilczek F 2012 Phys. Rev. Lett. 109 160401 doi: 10.1103/PhysRevLett.109.160401

    CrossRef Google Scholar

    [2]
    Shapere A and Wilczek F 2012 Phys. Rev. Lett. 109 160402 doi: 10.1103/PhysRevLett.109.160402

    CrossRef Google Scholar

    [3]
    Li T, Gong Z X, Yin Z Q, Quan H T, Yin X, Zhang P, Duan L M and Zhang X 2012 Phys. Rev. Lett. 109 163001 doi: 10.1103/PhysRevLett.109.163001

    CrossRef Google Scholar

    [4]
    Wilczek F 2013 Phys. Rev. Lett. 111 250402 doi: 10.1103/PhysRevLett.111.250402

    CrossRef Google Scholar

    [5]
    Sacha K 2015 Phys. Rev. A 91 033617 doi: 10.1103/PhysRevA.91.033617

    CrossRef Google Scholar

    [6]
    Else D V, Bauer B and Nayak C 2016 Phys. Rev. Lett. 117 090402 doi: 10.1103/PhysRevLett.117.090402

    CrossRef Google Scholar

    [7]
    Khemani V, Lazarides A, Moessner R and Sondhi S L 2016 Phys. Rev. Lett. 116 250401 doi: 10.1103/PhysRevLett.116.250401

    CrossRef Google Scholar

    [8]
    Yao N Y, Potter A C, Potirniche I D and Vishwanath A 2017 Phys. Rev. Lett. 118 030401 doi: 10.1103/PhysRevLett.118.030401

    CrossRef Google Scholar

    [9]
    Syrwid A, Zakrzewski J and Sacha K 2017 Phys. Rev. Lett. 119 250602 doi: 10.1103/PhysRevLett.119.250602

    CrossRef Google Scholar

    [10]
    Khemani V, von Keyserlingk C W and Sondhi S L 2017 Phys. Rev. B 96 115127 doi: 10.1103/PhysRevB.96.115127

    CrossRef Google Scholar

    [11]
    Russomanno A, Iemini F, Dalmonte M and Fazio R 2017 Phys. Rev. B 95 214307 doi: 10.1103/PhysRevB.95.214307

    CrossRef Google Scholar

    [12]
    Gong Z, Hamazaki R and Ueda M 2018 Phys. Rev. Lett. 120 040404 doi: 10.1103/PhysRevLett.120.040404

    CrossRef Google Scholar

    [13]
    Huang B, Wu Y H and Liu W V 2018 Phys. Rev. Lett. 120 110603 doi: 10.1103/PhysRevLett.120.110603

    CrossRef Google Scholar

    [14]
    Sacha K and Zakrzewski J 2018 Rep. Prog. Phys. 81 016401 doi: 10.1088/1361-6633/aa8b38

    CrossRef Google Scholar

    [15]
    Iemini F, Russomanno A, Keeling J, Schirò M, Dalmonte M and Fazio R 2018 Phys. Rev. Lett. 121 035301 doi: 10.1103/PhysRevLett.121.035301

    CrossRef Google Scholar

    [16]
    Kozin V K and Kyriienko O 2019 Phys. Rev. Lett. 123 210602 doi: 10.1103/PhysRevLett.123.210602

    CrossRef Google Scholar

    [17]
    Chew A, Mross D F and Alicea J 2019 arXiv:1907.12570

    Google Scholar

    [18]
    Bruno P 2013 Phys. Rev. Lett. 111 070402 doi: 10.1103/PhysRevLett.111.070402

    CrossRef Google Scholar

    [19]
    Watanabe H and Oshikawa M 2015 Phys. Rev. Lett. 114 251603 doi: 10.1103/PhysRevLett.114.251603

    CrossRef Google Scholar

    [20]
    Choi S, Landig R, Kucsko G, Zhou H, Isoya J, Jelezko F, Onoda S, Sumiya H, Khemani V, von Keyserlingk C 2017 Nature 543 221 doi: 10.1038/nature21426

    CrossRef Google Scholar

    [21]
    Zhang J, Hess P W, Kyprianidis A, Becker P, Lee A, Smith J, Pagano G, Potirniche I D, Potter A C, Vishwanath A 2017 Nature 543 217 doi: 10.1038/nature21413

    CrossRef Google Scholar

    [22]
    Ruderman M A and Kittel C 1954 Phys. Rev. 96 99 doi: 10.1103/PhysRev.96.99

    CrossRef Google Scholar

    [23]
    Kasuya T 1956 Prog. Theor. Phys. 16 45 doi: 10.1143/PTP.16.45

    CrossRef Google Scholar

    [24]
    Yosida K 1957 Phys. Rev. 106 893 doi: 10.1103/PhysRev.106.893

    CrossRef Google Scholar

    [25]
    Kozii V and Fu L 2017 arXiv:1708.05841

    Google Scholar

    [26]
    Cai Z, Schollwöck U and Pollet L 2014 Phys. Rev. Lett. 113 260403 doi: 10.1103/PhysRevLett.113.260403

    CrossRef Google Scholar

    [27]
    Prokof'ev N V, Svistunov B V and Tupitsyn I S 1998 Phys. Lett. A 238 253 doi: 10.1016/S0375-96019700957-2

    CrossRef Google Scholar

    [28]
    Mukhin S 2009 J. Supercond. Novel Magn. 22 75 doi: 10.1007/s10948-008-0358-4

    CrossRef Google Scholar

    [29]
    Galitski V 2010 Phys. Rev. B 82 054511 doi: 10.1103/PhysRevB.82.054511

    CrossRef Google Scholar

    [30]
    DeSalvo B, Patel K, Cai G and Chin C 2019 Nature 568 61 doi: 10.1038/s41586-019-1055-0

    CrossRef Google Scholar

  • Other Related Supplements

Catalog

    Article views (1145) PDF downloads (1097) Cited by()

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return