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

Abstract

We outline a general formalism of hydrodynamics for quantum systems with multiple particle species which undergo completely elastic scattering. In the thermodynamic limit, the complete kinematic data of the problem consists of the particle content, the dispersion relations, and a universal dressing transformation which accounts for interparticle interactions. We consider quantum integrable models and we focus on the one-dimensional fermionic 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, and establish a generalized detailed balance condition for a general quantum integrable model. We present the first exact analytic expressions for the general Drude weights in the Hubbard model, and explain how to reconcile different approaches for computing Drude weights from the previous literature.

4 pages + supplemental material

References in corpus (12)

• Open XXZ spin chain: Nonequilibrium steady state and strict bound on ballistic transport
• Spin transport in a one-dimensional anisotropic Heisenberg model
• Conservation laws, integrability and transport in one-dimensional quantum systems
• From Interacting Particles to Equilibrium Statistical Ensembles
• Diffusive high-temperature transport in the one-dimensional Hubbard model
• Exact solution for the quench dynamics of a nested integrable system
• Transport properties of the one-dimensional Hubbard model at finite temperature
• Proposal for measuring the finite-temperature Drude weight of integrable systems
• Hubbard-to-Heisenberg crossover (and efficient computation) of Drude weights at low temperatures
• Real-time dynamics in the one-dimensional Hubbard model
• Non-equilibrium thermal transport and vacuum expansion in the Hubbard model
• Synergetic effect of spin-orbit coupling and Zeeman splitting on the optical conductivity in the one-dimensional Hubbard model

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• On Classical Integrability of the Hydrodynamics of Quantum Integrable Systems
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• Kinetic theory of quantum and classical Toda lattices
• Generalized Hydrodynamic approach to charge and energy currents in the one-dimensional Hubbard model
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• A diagrammatic approach towards the thermodynamics of integrable systems