Diffusion and ballistic transport in one-dimensional quantum systems

TL;DR

This paper demonstrates that diffusion is a universal feature in interacting one-dimensional quantum systems with a lattice, challenging the belief that such systems are solely ballistic, and provides theoretical and numerical evidence aligning with experimental observations.

Contribution

It reveals that diffusion occurs universally in 1D quantum systems with a lattice and offers a parameter-free formula for the spin-lattice relaxation rate.

Findings

Diffusion is universally present in 1D systems with a lattice.

The derived formula matches experimental data.

Long-lived current decay persists at high temperatures.

Abstract

It has been conjectured that transport in integrable one-dimensional (1D) systems is necessarily ballistic. The large diffusive response seen experimentally in nearly ideal realizations of the S=1/2 1D Heisenberg model is therefore puzzling and has not been explained so far. Here, we show that, contrary to common belief, diffusion is universally present in interacting 1D systems subject to a periodic lattice potential. We present a parameter-free formula for the spin-lattice relaxation rate which is in excellent agreement with experiment. Furthermore, we calculate the current decay directly in the thermodynamic limit using a time-dependent density matrix renormalization group algorithm and show that an anomalously large time scale exists even at high temperatures.