Coexistence of diffusive and ballistic transport in integrable quantum lattice models

TL;DR

This study examines high-temperature charge transport in two integrable quantum models, revealing complex spectral features and questioning the presence of diffusive transport in certain regimes.

Contribution

It introduces an upgraded microcanonical Lanczos method to analyze finite-size systems and provides detailed spectral analysis of conductivity in integrable models.

Findings

No clear evidence of diffusive transport at specific anisotropy values.

Spectral fine structures are linked to anisotropy parameter variations.

Universal behavior observed in the Hubbard model away from half-filling.

Abstract

We investigate the high-temperature dynamical conductivity $\sigma(\omega)$ in two one-dimensional integrable quantum lattice models: the anisotropic XXZ spin chain and the Hubbard chain. The emphasis is on the metallic regime of both models, where besides the ballistic component, the regular part of conductivity might reveal a diffusive-like transport. To resolve the low-frequency dynamics, we upgrade the microcanonical Lanczos method enabling studies of finite-size systems with up to $L\leq 32$ sites for XXZ spin model with the frequency resolution $\delta \omega \sim 10^{-3} J$. Results for the XXZ chain reveal a fine structure of $\sigma(\omega)$ spectra, which originates from the discontinuous variation of the stiffness, previously found at commensurate values of the anisotropy parameter $\Delta$. Still, we do not find a clear evidence for a diffusive component, at least not for commensurate values of $\Delta$, particularly for $\Delta =0.5$, as well as for $\Delta \to 0$. Similar is the conclusion for the Hubbard model away from half-filling, where the spectra reveal more universal behavior.