A multi-fragment real-time extension of projected density matrix embedding theory: Non-equilibrium electron dynamics in extended systems

TL;DR

This paper introduces a real-time extension of projected density matrix embedding theory (pDMET) for simulating non-equilibrium electron dynamics in large, strongly correlated systems, showing improved accuracy and convergence over existing methods.

Contribution

The authors develop a multi-fragment real-time pDMET that enables efficient simulation of non-equilibrium dynamics in extended strongly correlated systems, extending static pDMET to time-dependent scenarios.

Findings

Large improvement over TDHF in accuracy.

Rapid convergence to exact dynamics with increasing fragment size.

Effective simulation of impurity models with disordered distributions.

Abstract

In this work, we derive a multi-fragment real-time extension of projected density matrix embedding theory (pDMET) designed to treat non-equilibrium electron dynamics in strongly correlated systems. As in the previously developed static pDMET, real-time pDMET partitions the total system into many fragments; the coupling between each fragment and the rest of the system is treated through a compact representation of the environment in terms of a quantum bath. Real-time pDMET involves simultaneously propagating the wavefunctions for each separate fragment-bath embedding system along with an auxiliary mean-field wavefunction of the total system. The equations of motion are derived by (i) projecting the time-dependent Schrodinger equation in the fragment and bath space associated with each separate fragment and by (ii) enforcing the pDMET matching conditions between the global 1-particle reduced density matrix (1-RDM) obtained from the fragment calculations and the mean-field 1-RDM at all points in time. The accuracy of the method is benchmarked through comparisons to the time-dependent density-matrix renormalization group (TD-DMRG) and time-dependent Hartree-Fock (TDHF) theory; the methods were applied to a single-impurity Anderson model and multi-impurity Anderson models with ordered and disordered distributions of the impurities. The results demonstrate a large improvement over TDHF and rapid convergence to the exact dynamics with an increase in fragment size. Our results demonstrate that real-time pDMET is a promising and flexible method to simulate non-equilibrium electron dynamics in heterogeneous systems of large size.