Successes and Failures of Kadanoff-Baym Dynamics in Hubbard Nanoclusters

TL;DR

This paper evaluates various many-body approximations for simulating the non-equilibrium dynamics of small Hubbard nanoclusters, finding the T-matrix approximation most accurate in low-density regimes but noting unphysical steady states at long times.

Contribution

It systematically compares the accuracy of Hartree-Fock, 2nd Born, GW, and T-matrix approximations against exact solutions for Hubbard nanoclusters, highlighting the T-matrix's advantages.

Findings

T-matrix approximation closely matches exact results in low-density regimes.

Most approximations lead to unphysical steady states at long times.

T-matrix outperforms other methods overall.

Abstract

We study the non-equilibrium dynamics of small, strongly correlated clusters, described by a Hubbard Hamiltonian, by propagating in time the Kadanoff-Baym equations within the Hartree-Fock, 2nd Born, GW and T-matrix approximations. We compare the results to exact numerical solutions. We find that the T-matrix is overall superior to the other approximations, and is in good agreement with the exact results in the low-density regime. In the long time limit, the many-body approximations attain an unphysical steady state which we attribute to the implicit inclusion of infinite order diagrams in a few-body system.