# Microscopic origin of ideal conductivity in integrable quantum models

## TL;DR

This paper explains the microscopic origin of perfect conductivity in integrable quantum models using group theory and hydrodynamics, providing a new computational method and revealing fractal dependence on anisotropy.

## Contribution

It introduces a rigorous group-theoretic and hydrodynamic framework to understand and compute ideal conductivities in integrable quantum systems, resolving longstanding controversies.

## Key findings

- Exact Drude weights calculated for the anisotropic Heisenberg model.
- Discontinuous, fractal dependence of spin Drude weight on anisotropy.
- Efficient method for studying transport in integrable models at finite temperatures.

## Abstract

Non-ergodic dynamical systems display anomalous transport properties. A prominent example are integrable quantum systems, whose exceptional property are diverging DC conductivities. In this Letter, we explain the microscopic origin of ideal conductivity by resorting to the thermodynamic particle content of a system. Using group-theoretic arguments we rigorously resolve the long-standing controversy regarding the nature of spin and charge Drude weights in the absence of chemical potentials. In addition, by employing a hydrodynamic description, we devise an efficient computational method to calculate exact Drude weights from the stationary currents generated in an inhomogeneous quench from bi-partitioned initial states. We exemplify the method on the anisotropic Heisenberg model at finite temperatures for the entire range of anisotropies, accessing regimes which are out of reach with other approaches. Quite remarkably, spin Drude weight and asymptotic spin current rates reveal a completely discontinuous (fractal) dependence on the anisotropy parameter.