Superdiffusive transport of energy in one-dimensional metals

Understand

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.