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

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.

Figures (7)

• Figure 1: Full phase diagram represented by the contour plot of (a) charge (b) spin and (c) cross DWs at temperature $T=0.005$ and $u=1$. The dotted lines represent analytic solutions of BA equations obtained at zero temperature. The white dashed lines are the contour lines at $D^{cc},D^{ss}=0.38,0.4355$ and $D^{cs}=0.05,0.2$. Phases I to V correspond to vacuum, fully polarized partially filled, fully polarized half filled, partially polarized partially filled, and partially polarized half filled, respectively. The charge and cross DWs cannot distinguish phases III and V, which are the two Mott phases of charge insulator. For the two fully polarized phases (II and III), there is no distinction between spin and charge and, hence, all three DWs are the same.
• Figure 2: Luttinger parameters vs chemical potential for $B=0.6$ and $u=1$ in the ground state.
• Figure 3: Ground-state DWs as functions of interaction strength $u$ at the filling factor $n_c=0.5$ and for two different magnetization densities $m=0$ and $m=0.1$. All lines are analytic results of Eqs. (\ref{['dc-ds-bm']}).
• Figure 4: $D^{se}$ (a) and $D^{ce}$ (b) as functions of chemical potential $\mu$ for different temperatures $T$ at $B=0.5,u=1$. The critical fields $\mu_{c1},\mu_{c2}$, indicated as vertical black dashed lines, are boundaries for II-IV and IV-V, respectively.
• Figure S1: The scaling behavior of $D^{ss}$ versus magnetic field $B$ for the phase transitoin II-IV with $u=1$, $\mu=-0.8382$. The critical magnetic field for this transition is $B_c=0.8282$, as indicated by the dashed vertical line. The analytical results (solid lines) based on Eqs. (\ref{['24s']}) and (\ref{['24c']}) are in excellent agreement with numerical solutions (symbols) of the TBA equations.