Chin. Phys. Lett.  2020, Vol. 37 Issue (5): 050503    DOI: 10.1088/0256-307X/37/5/050503
Imaginary Time Crystal of Thermal Quantum Matter
Zi Cai1,2**, Yizhen Huang1, W. Vincent Liu3,4,2**
1Wilczek Quantum Center and Key Laboratory of Artificial Structures and Quantum Control, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240
2Shanghai Research Center for Quantum Sciences, Shanghai 201315
3Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
4Wilczek Quantum Center, School of Physics and Astronomy and T. D. Lee Institute, Shanghai Jiao Tong University, Shanghai 200240
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Zi Cai, Yizhen Huang, W. Vincent Liu 2020 Chin. Phys. Lett. 37 050503
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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 $\beta$ is formally equivalent to a dynamic system evolving along an imaginary time from 0 to $i\beta$ 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.
Received: 08 April 2020      Published: 25 April 2020
PACS:  05.30.Jp (Boson systems)  
  02.70.Ss (Quantum Monte Carlo methods)  
  03.65.Yz (Decoherence; open systems; quantum statistical methods)  
Fund: 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).
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Zi Cai
Yizhen Huang
W. Vincent Liu
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