Phys. Rev. B 107, 214302 (2023)

Classical phase space crystals in an open environment

Ali Emami Kopaei ^2,3, Krzysztof Sacha ^3,4, and Lingzhen Guo ^1,5,* 

1 Center for Joint Quantum Studies and Department of Physics, School of Science, Tianjin University, 92 Weijin Road, Tianjin 300072, China

2 Szkoła Doktorska Nauk Scisłych i Przyrodniczych, Wydział Fizyki, Astronomii i Informatyki Stosowanej, Uniwersytet Jagiellon ́ski, ulica Profesora Stanisława Łojasiewicza 11, PL-30-348 Kraków, Poland

3 Instytut Fizyki Teoretycznej, Wydział Fizyki, Astronomii i Informatyki Stosowanej, Uniwersytet Jagiellonski, uli-ca Profesora Stanisława Łojasiewicza 11, PL-30-348 Kraków, Poland

4 Centrum Marka Kaca, Uniwersytet Jagiellon ́ski, ulica Profesora Stanisława Łojasiewicza 11, PL-30-348 Kraków, Poland

5 Max Planck Institute for the Science of Light, Staudtstrasse 2, 91058 Erlangen, Germany

* Author to whom correspondence should be addressed: lingzhen_guo@tju.edu.cn

Abstract

It was recently discovered that a crystalline many-body state can exist in the phase space of a closed dynamical system. A phase space crystal can be an anomalous Chern insulator that supports chiral topological transport without breaking physical time-reversal symmetry [L. Guo et al., Phys. Rev. B 105, 094301 (2022)]. In this work, we further study the effects of an open dissipative environment with thermal noise and identify the existence condition of classical phase space crystals in realistic scenarios. By defining a crystal order parameter, we plot the phase diagram in the parameter space of dissipation rate, interaction, and temperature. Our present work paves the way to realize phase space crystals and explore anomalous chiral transport in experiments.