Quantum transport in 1D Hubbard model: Drude weights and Seebeck effect

TL;DR

This paper provides exact calculations of Drude weights and Seebeck effects in the 1D Hubbard model, revealing universal scaling laws and spin-charge coupling effects, advancing understanding of quantum transport in strongly correlated systems.

Contribution

It offers the first exact computation of Drude weights and Seebeck effects for the 1D Hubbard model across various parameters using quantum integrability.

Findings

Exact Drude weights and Seebeck effects calculated for the 1D Hubbard model.

Universal scaling laws for Drude weights across phase transitions.

Identification of spin-charge coupling effects influencing transport properties.

Abstract

The Drude weight (DW) is an essential quantity that characterizes the quantum transport properties of many-body systems. However, a rigorous understanding and exact computation of DWs, particularly for strongly correlated systems with doping, still remain elusive. In this Letter, taking advantage of the quantum integrability, we calculate exactly the DWs and Seebeck effect (SE) for generic filling factor in one-dimensional (1D) Fermi-Hubbard model with arbitrary interaction strengths and magnetic fields. We build up its intrinsic connection to the Luttinger parameters, and derive universal scaling laws for DWs across phase transitions. Our results provide a deep understanding of mutual influences in transport between the spin and the charge degrees of freedom, showing a counterintuitive subtle spin-charge coupling effect and uncovering the microscopic origin of the (spin) Seebeck effects in thermal conductivity. Finally, we propose an experimental protocol to measure the DWs in ultracold atomic systems.