Decay of currents for strong interactions

TL;DR

This paper studies how strong interactions cause current decay in quantum systems, showing that relaxation follows a Gaussian pattern and the diffusion coefficient inversely scales with interaction strength, supported by numerical simulations.

Contribution

It demonstrates that current relaxation in strongly interacting quantum systems can be accurately described by perturbation theory, revealing Gaussian decay and inverse scaling of diffusion with interaction strength.

Findings

Current decay is well described by Gaussian relaxation.

Diffusion coefficient scales approximately with the inverse of interaction strength.

Numerical results confirm theoretical predictions across various models.

Abstract

The decay of current autocorrelation functions is investigated for quantum systems featuring strong 'interactions'. Here, the term interaction refers to that part of the Hamiltonian causing the (major) decay of the current. On the time scale before the (first) zero-crossing of the current, its relaxation is shown to be well described by a suitable perturbation theory in the lowest orders of the interaction strength, even and especially if interactions are strong. In this description the relaxation is found to be rather close to a Gaussian decay and the resulting diffusion coefficient approximately scales with the inverse interaction strength. These findings are also confirmed by numerical results from exact diagonalization for several one-dimensional transport models including spin transport in the Heisenberg chain w.r.t. different spin quantum numbers, anisotropy, next-to-nearest-neighbor interaction, or alternating magnetic field; energy transport in the Ising chain with tilted magnetic field; and transport of excitations in a randomly coupled modular quantum system. The impact of these results for weak interactions is finally discussed.