Nonequilibrium dynamical cluster theory

TL;DR

This paper introduces a nonequilibrium dynamical cluster theory to study spatially nonlocal correlations in interacting fermions, revealing momentum-dependent relaxation dynamics and improved predictions over traditional methods.

Contribution

The authors develop a cluster generalization of nonequilibrium DMFT, enabling analysis of nonlocal correlations in fermionic systems during nonequilibrium processes.

Findings

Double occupancy thermalizes quickly in 1D and 2D.

Momentum distribution relaxes on longer timescales.

Relaxation is momentum-dependent, faster near certain points.

Abstract

We study the effect of spatially nonlocal correlations on the nonequilibrium dynamics of interacting fermions by constructing the nonequilibrium dynamical cluster theory, a cluster generalization of the nonequilibrium dynamical mean-field theory (DMFT). The formalism is applied to interaction quenches in the Hubbard model in one and two dimensions, and the results are compared with data from single-site DMFT, the time-dependent density matrix renormalization group, and lattice perturbation theory. Both in one and two dimensions the double occupancy quickly thermalizes, while the momentum distribution relaxes only on much longer time scales. For the two-dimensional square lattice we find a strongly momentum-dependent evolution of the momentum distribution around the Fermi energy, with a much faster relaxation near the momenta $(0,\pi)$ and $(\pi,0)$ than near $(\pi/2,\pi/2)$. This result is interpreted as reflecting the momentum-anisotropic quasiparticle lifetime of the marginal Fermi liquid. The method is further applied to the two-dimensional Hubbard model driven by a dc electric field, where the damping of the Bloch oscillation of the current is found to be less effective than predicted by DMFT and lattice perturbation theory.