# Superdiffusive transport of energy in one-dimensional metals

## TL;DR

This paper demonstrates that in one-dimensional metals with integrability-breaking interactions, energy spreads superdiffusively, exhibiting behavior between diffusion and ballistic transport, which can be observed experimentally.

## Contribution

It combines analytical models and numerical simulations to show superdiffusive energy transport in realistic 1D metals, extending understanding beyond ideal integrable systems.

## Key findings

- Energy spreads superdiffusively in non-integrable 1D metals.
- Superdiffusive behavior is stable and experimentally observable.
- Different metals exhibit varying scaling exponents and shapes.

## Abstract

Metals in one spatial dimension are described at the lowest energy scales by the Luttinger liquid theory. It is well understood that this free theory, and even interacting integrable models, can support ballistic transport of conserved quantities including energy. In contrast, realistic one-dimensional metals, even without disorder, contain integrability-breaking interactions that are expected to lead to thermalization and conventional diffusive linear response. We argue that the expansion of energy when such a non-integrable Luttinger liquid is locally heated above its ground state shows superdiffusive behavior (i.e., spreading of energy that is intermediate between diffusion and ballistic propagation), by combining an analytical anomalous diffusion model with numerical matrix product state calculations on a specific perturbed spinless fermion chain. Different metals will have different scaling exponents and shapes in their energy spreading, but the superdiffusive behavior is stable and should be visible in time-resolved experiments.