Temperature dependence of charge transport in the half-filled 1D Hubbard model

Finite-temperature T>0 transport properties of integrable and nonintegrable one-dimensional (1D) many-particle quantum systems are rather different, showing in the metallic phases ballistic and diffusive behavior, respectively. The repulsive 1D Hubbard model is an integrable system of wide physical interest. For electronic densities $n\neq1$ it is an ideal conductor, with ballistic charge transport for T larger or equal to 0. In spite that it is solvable by the Bethe ansatz, ...

Whether in the thermodynamic limit of lattice length infinite, hole concentration tending to zero, nonzero temperature, and U/t > 0 the charge stiffness of the 1D Hubbard model with first neighbor transfer integral t and on-site repulsion U is finite or vanishes and thus whether there is or there is no ballistic charge transport, respectively, remains an unsolved and controversial issue, as different approaches yield contradictory results. In this paper we provide an upper bo...

We identify a class of one-dimensional spin and fermionic lattice models which display diverging spin and charge diffusion constants, including several paradigmatic models of exactly solvable strongly correlated many-body dynamics such as the isotropic Heisenberg spin chains, the Fermi-Hubbard model, and the t-J model at the integrable point. Using the hydrodynamic transport theory, we derive an analytic lower bound on the spin and charge diffusion constants by calculating th...

We consider charge and spin transport in the one-dimensional Hubbard model at infinite temperature, half-filling and zero magnetization. Implementing matrix-product-operator simulations of the non-equilibrium steady states of boundary-driven open Hubbard chains for up to 100 sites we find clear evidence of diffusive transport for any (non-zero and finite) value of the interaction U.

We study finite-temperature transport properties of the one-dimensional Hubbard model using the density matrix renormalization group. Our aim is two-fold: First, we compute both the charge and the spin current correlation function of the integrable model at half filling. The former decays rapidly, implying that the corresponding Drude weight is either zero or very small. Second, we calculate the optical charge conductivity sigma(omega) in presence of small integrability-break...

We study the charge conductivity of the one-dimensional repulsive Hubbard model at finite temperature using the method of dynamical quantum typicality, focusing at half filling. This numerical approach allows us to obtain current autocorrelation functions from systems with as many as 18 sites, way beyond the range of standard exact diagonalization. Our data clearly suggest that the charge Drude weight vanishes with a power law as a function of system size. The low-frequency d...

Transport through a 1D Mott-Hubbard insulator of a finite length $L$ is studied beyond perturbative approach. At special value of the low energy constant of the interaction we have mapped the problem onto the exactly solvable models and found current vs. voltage $V$ at high temperature $T>max(m,T_L)$ and at low energy $T,V<T_L$ ($T_L=v_c/L$; $v_c:$ charge velocity). The result shows that for the strong interaction creating a large Mott-Hubbard gap $2m \gg T_L $ inside the wir...

We present results for the zero and finite temperature Drude weight D(T) and for the Meissner fraction of the attractive and the repulsive Hubbard model, as well as for the model with next nearest neighbor repulsion. They are based on Quantum Monte Carlo studies and on the Bethe ansatz. We show that the Drude weight is well defined as an extrapolation on the imaginary frequency axis, even for finite temperature. The temperature, filling, and system size dependence of D is obt...

In this Chapter, we present recent theoretical developments on the finite temperature transport of one dimensional electronic and magnetic quantum systems as described by a variety of prototype models. In particular, we discuss the unconventional transport and dynamic - spin, electrical, thermal - properties implied by the integrability of models as the spin-1/2 Heisenberg chain or Hubbard. Furthermore, we address the implication of these developments to experimental studies ...

The Hubbard model describes interacting electrons on a lattice,a situation which occurs in various solid state materials and devices. The aim of the present paper is to briefly discuss this model and its applications in the study of transport properties of Q1D and Q2D systems. Several examples are taken from materials and fields that have been intensively studied in recent years.