Eur. Phys. J. A (2020) 56: 111
https://doi.org/10.1140/epja/s10050-020-00119-7

Regular Article –Theoretical Physics

Combining phase-space and time-dependent reduced density matrix approach to describe the dynamics of interacting fermions

¹ Université Paris-Saclay, CNRS/IN2P3, IJCLab, 91405, Orsay, France
² Centre de mathématiques et de leurs applications, CNRS, ENS Paris-Saclay, Université Paris-Saclay, 94235, Cachan Cedex, France
³ Physics Department, Faculty of Sciences, Ankara University, 06100, Ankara, Turkey

^* e-mail: lacroix@ipno.in2p3.fr

Received: 4 February 2020
Accepted: 21 February 2020
Published online: 8 April 2020

Abstract

The possibility to apply phase-space methods to many-body interacting systems might provide accurate descriptions of correlations with a reduced numerical cost. For instance, the so-called stochastic mean-field phase-space approach, where the complex dynamics of interacting fermions is replaced by a statistical average of mean-field like trajectories is able to grasp some correlations beyond the mean-field. We explore the possibility to use alternative equations of motion in the phase-space approach. Guided by the BBGKY hierarchy, equations of motion that already incorporate part of the correlations beyond mean-field are employed along each trajectory. The method is called hybrid phase-space because it mixes phase-space techniques and the time-dependent reduced density matrix approach. The novel approach is applied to the one-dimensional Fermi–Hubbard model. We show that the predictive power is improved compared to the original stochastic mean-field method. In particular, in the weak-coupling regime, the results of the HPS theory can hardly be distinguished from the exact solution even for long time.