Ballistic transport in the one-dimensional Hubbard model: hydrodynamic approach

Enej Ilievski, Jacopo De Nardis

Published 2017-06-19Version 1

We outline a general formalism of hydrodynamics for quantum systems with multiple particle species which undergo completely elastic scattering. In the thermodynamic limit, a complete kinematic data of the problem consists the particle content, their dispersion relations, and a universal dressing transformation which accounts for interparticle interactions. We consider quantum integrable models and we focus on the one-dimensional femionic Hubbard model. By linearizing hydrodynamic equations, we provide exact closed-form expressions for Drude weights, generalized static charge susceptibilities and charge-current correlators valid on hydrodynamic scale, represented as integral kernels operating diagonally in the space of mode numbers of thermodynamic excitations. We find that on hydrodynamic scales Drude weights manifestly display Onsager reciprocal relations even for generic (i.e. non-canonical) equilibrium states, describing a generalized detailed balance condition in a general integrable model. Our results reconcile different approaches for computing Drude weights found in the previous literature.