Non-equilibrium correlation dynamics in the one-dimensional Fermi-Hubbard model: A testbed for the two-particle reduced density matrix theory

TL;DR

This study assesses the effectiveness of the time-dependent two-particle reduced density matrix (TD2RDM) theory in accurately modeling the non-equilibrium dynamics of a one-dimensional Fermi-Hubbard system, highlighting the importance of three-particle correlation reconstruction.

Contribution

It demonstrates that TD2RDM can reliably simulate non-equilibrium dynamics in correlated fermionic systems, emphasizing the role of three-particle cumulant reconstruction for accuracy.

Findings

TD2RDM accurately captures non-equilibrium dynamics from weak to moderate correlations.

The quality of three-particle cumulant reconstruction is crucial for the method's accuracy.

Critical parameters include the size of induced three-particle correlations and cross correlations.

Abstract

We explore the non-equilibrium dynamics of a one-dimensional Fermi-Hubbard system as a sensitive testbed for the capabilities of the time-dependent two-particle reduced density matrix (TD2RDM) theory to accurately describe time-dependent correlated systems. We follow the time evolution of the out-of-equilibrium finite-size Fermi-Hubbard model initialized by a quench over extended periods of time. By comparison with exact calculations for small systems and with matrix product state (MPS) calculations for larger systems but limited to short times, we demonstrate that the TD2RDM theory can accurately account for the non-equilibrium dynamics in the regime from weak to moderately strong inter-particle correlations. We find that the quality of the approximate reconstruction of the three-particle cumulant (or correlation) required for the closure of the equations of motion for the reduced density matrix is key to the accuracy of the numerical TD2RDM results. We identify the size of the dynamically induced three-particle correlations and the amplitude of cross correlations between the two- and three-particle cumulants as critical parameters that control the accuracy of the TD2RDM theory when current state-of-the art reconstruction functionals are employed.