Hubbard Interactions From Density-Functional Perturbation Theory

Manuel Kreye

We advance perturbative approaches for out-of-equilibrium quantum many-body systems by applying unitary perturbation theory to the real-time evolution of the weakly interacting Hubbard model in d > 1 dimensions. We derive general expressions for the fermionic operators that allow us to perturbatively calculate the time evolution of observables to second-order expansion in the interaction strength. We find that the results are stable up to and including the prethermalization regime. We apply our findings to the nonequilibrium build-up of density-density correlations after a weak interaction quench and compare the prethermalization values to equilibrium correlations. Furthermore, we analyze the light-cone-like structure of the density-density susceptibility and the equal-time correlation function in the context of the Lieb-Robinson bounds.

S. Pairault, David Sénéchal, A.–M. S. Tremblay

Gergely T. Zimányi, Elihu Abrahams

Miroslav Hopjan, Daniel Karlsson, Simon Ydman +2 more

We propose a description of nonequilibrium systems via a simple protocol that combines exchange-correlation potentials from density functional theory with self-energies of many-body perturbation theory. The approach, aimed to avoid double counting of interactions, is tested against exact results in Hubbard-type systems, with respect to interaction strength, perturbation speed and inhomogeneity, and system dimensionality and size. In many regimes, we find significant improvement over adiabatic time dependent density functional theory or second Born nonequilibrium Green's function approximations. We briefly discuss the reasons for the residual discrepancies, and directions for future work.

M. Ulmke

Jize Zhao, Kazuo Ueda, Xiaoqun Wang

We investigate low-energy excitations of the one-dimensional half-filled SU(4) Hubbard model with an attractive on-site interaction $U<0$ using the density-matrix renormalization-group method as well as perturbation theory. We find that the ground state is a charge-density-wave state with long-range order. The ground state is completely incompressible since all the excitations are gapful. The charge gap, which is the same as the four-particle excitation gap, is a nonmonotonic function of $U$, while the spin gap and others increase with increasing $\ensuremath{\mid}U\ensuremath{\mid}$ and have linear asymptotic behaviors.