Performance of wave function and Green's functions based methods for non equilibrium many-body dynamics

TL;DR

This paper compares wave function and Green's function methods for modeling non-equilibrium quantum many-body dynamics, highlighting their strengths and limitations under different driving field intensities.

Contribution

It provides a critical comparison of explicit, compressed, and Green's function approaches for non-equilibrium dynamics, with numerically exact benchmarks.

Findings

Coupled cluster is accurate for weak fields but struggles with strong driving.

Green's function GW approximation improves over mean-field in strong fields.

Strong entanglement occurs under intense driving, affecting method accuracy.

Abstract

Theoretical descriptions of non equilibrium dynamics of quantum many-body systems essentially employ either (i) explicit treatments, relying on truncation of the expansion of the many-body wave function, (ii) compressed representations of the many-body wave function, or (iii) evolution of an effective (downfolded) representation through Green's functions. In this work, we select representative cases of each of the methods and address how these complementary approaches capture the dynamics driven by intense field perturbations to non equilibrium states. Under strong driving, the systems are characterized by strong entanglement of the single particle density matrix and natural populations approaching those of a strongly interacting equilibrium system. We generate a representative set of results that are numerically exact and form a basis for critical comparison of the distinct families of methods. We demonstrate that the compressed formulation based on similarity transformed Hamiltonians (coupled cluster approach) is practically exact in weak fields and, hence, weakly or moderately correlated systems. Coupled cluster, however, struggles for strong driving fields, under which the system exhibits strongly correlated behavior, as measured by the von Neumann entropy of the single particle density matrix. The dynamics predicted by Green's functions in the (widely popular) GW approximation are less accurate by improve significantly upon the mean-field results in the strongly driven regime.