Signatures of integrability in charge and thermal transport in 1D quantum systems

TL;DR

This paper investigates how integrability affects charge and thermal transport in one-dimensional quantum systems, revealing ballistic behavior in integrable models and diffusive behavior in non-integrable ones through numerical analysis.

Contribution

It provides a detailed numerical comparison of transport properties in integrable and non-integrable 1D quantum models, highlighting signatures of integrability in dynamical conductivities.

Findings

Drude weight indicates ballistic transport in integrable systems.

Meissner stiffness diminishes with system size in both systems.

Dynamical conductivities show contrasting behaviors consistent with integrability.

Abstract

Integrable and non-integrable systems have very different transport properties. In this work, we highlight these differences for specific one dimensional models of interacting lattice fermions using numerical exact diagonalization. We calculate the finite temperature adiabatic stiffness (or Drude weight) and isothermal stiffness (or ``Meissner'' stiffness) in electrical and thermal transport and also compute the complete momentum and frequency dependent dynamical conductivities $\sigma(q,\omega)$ and $\kappa(q,\omega)$. The Meissner stiffness goes to zero rapidly with system size for both integrable and non-integrable systems. The Drude weight shows signs of diffusion in the non-integrable system and ballistic behavior in the integrable system. The dynamical conductivities are also consistent with ballistic and diffusive behavior in the integrable and non-integrable systems respectively.