Express Letter
Imaginary Time Crystal of Thermal Quantum Matter
-
Abstract
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 is formally equivalent to a dynamic system evolving along an imaginary time from 0 to 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. -
-
References
[1] Wilczek F 2012 Phys. Rev. Lett. 109 160401 doi: 10.1103/PhysRevLett.109.160401[2] Shapere A and Wilczek F 2012 Phys. Rev. Lett. 109 160402 doi: 10.1103/PhysRevLett.109.160402[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[4] Wilczek F 2013 Phys. Rev. Lett. 111 250402 doi: 10.1103/PhysRevLett.111.250402[5] Sacha K 2015 Phys. Rev. A 91 033617 doi: 10.1103/PhysRevA.91.033617[6] Else D V, Bauer B and Nayak C 2016 Phys. Rev. Lett. 117 090402 doi: 10.1103/PhysRevLett.117.090402[7] Khemani V, Lazarides A, Moessner R and Sondhi S L 2016 Phys. Rev. Lett. 116 250401 doi: 10.1103/PhysRevLett.116.250401[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[9] Syrwid A, Zakrzewski J and Sacha K 2017 Phys. Rev. Lett. 119 250602 doi: 10.1103/PhysRevLett.119.250602[10] Khemani V, von Keyserlingk C W and Sondhi S L 2017 Phys. Rev. B 96 115127 doi: 10.1103/PhysRevB.96.115127[11] Russomanno A, Iemini F, Dalmonte M and Fazio R 2017 Phys. Rev. B 95 214307 doi: 10.1103/PhysRevB.95.214307[12] Gong Z, Hamazaki R and Ueda M 2018 Phys. Rev. Lett. 120 040404 doi: 10.1103/PhysRevLett.120.040404[13] Huang B, Wu Y H and Liu W V 2018 Phys. Rev. Lett. 120 110603 doi: 10.1103/PhysRevLett.120.110603[14] Sacha K and Zakrzewski J 2018 Rep. Prog. Phys. 81 016401 doi: 10.1088/1361-6633/aa8b38[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[16] Kozin V K and Kyriienko O 2019 Phys. Rev. Lett. 123 210602 doi: 10.1103/PhysRevLett.123.210602[17] Chew A, Mross D F and Alicea J 2019 arXiv:1907.12570[18] Bruno P 2013 Phys. Rev. Lett. 111 070402 doi: 10.1103/PhysRevLett.111.070402[19] Watanabe H and Oshikawa M 2015 Phys. Rev. Lett. 114 251603 doi: 10.1103/PhysRevLett.114.251603[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[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[22] Ruderman M A and Kittel C 1954 Phys. Rev. 96 99 doi: 10.1103/PhysRev.96.99[23] Kasuya T 1956 Prog. Theor. Phys. 16 45 doi: 10.1143/PTP.16.45[24] Yosida K 1957 Phys. Rev. 106 893 doi: 10.1103/PhysRev.106.893[25] Kozii V and Fu L 2017 arXiv:1708.05841[26] Cai Z, Schollwöck U and Pollet L 2014 Phys. Rev. Lett. 113 260403 doi: 10.1103/PhysRevLett.113.260403[27] Prokof'ev N V, Svistunov B V and Tupitsyn I S 1998 Phys. Lett. A 238 253 doi: 10.1016/S0375-96019700957-2[28] Mukhin S 2009 J. Supercond. Novel Magn. 22 75 doi: 10.1007/s10948-008-0358-4[29] Galitski V 2010 Phys. Rev. B 82 054511 doi: 10.1103/PhysRevB.82.054511[30] DeSalvo B, Patel K, Cai G and Chin C 2019 Nature 568 61 doi: 10.1038/s41586-019-1055-0 -
Supplements
Other Related Supplements
-
Cover image
212KB
-