Title: Quantum dynamics of correlated fermionic systems in the phase space representation
Polish Ministry of Science and Higher Education through a “Mobilność Plus” program nr 1651/MOB/V/2017/0
Realization period: 2018/07/01 - 2019/12/31
[1] "Semiclassical bounds on the dynamics of two-dimensional interacting disordered fermions"
Łukasz Iwanek, Marcin Mierzejewski, Anatoli Polkovnikov, Dries Sels, and Adam S. Sajna
Phys. Rev. B 107, 064202 (2023)
arXiv:2209.15062 (2023)
[2] "Slow semiclassical dynamics of a two-dimensional Hubbard model in disorder-free potentials"
Aleksander Kaczmarek, Adam S. Sajna
arXiv:2210.01082 (2022)
[3] "Semiclassical dynamics of a disordered two-dimensional Hubbard model with long-range interactions"
Adam S. Sajna, Anatoli Polkovnikov
Phys. Rev. A 102, 033338 (2020)
In the project phase space representation methods for fermionic particles were considered. We obtain efficient description of long-range interactions within the extended Hubbard model. This was achieved by finding proper phase space representation of underlying Hamiltonian. Method is asymptotically exact in the long range interaction limit and can be used to efficiently described e.g. Coulomb type of interactions. The number of degrees of freedom scales polynomially with the system size therefore it can be used to simulated dynamics in higher dimensional systems with many degrees of freedom.
We confirmed validity of the method by studying two-dimensional Hubbard system in disorder quenche protocol where truncated Wigner approximation was used. Interestingly, for weak disorder we get subdiffusion dynamics of charges while spin degrees of freedom show diffusion character. Different time scales was also observed for a time evolution of quantum Fisher information in the strong disorder limit. Moreover it was shown that some initial condition can strongly impact time scales of thermalization and therefore additionally slow down dynamics.