Absence of finite-temperature ballistic charge transport in the 1D half-filled Hubbard model

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 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...

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 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 paper we study the charge and spin currents transported by the elementary excitations of the one-dimensional Hubbard model. The corresponding current spectra are obtained by both analytic methods and numerical solution of the Bethe-ansatz equations. For the case of half-filling, we find that the spin-triplet excitations carry spin but no charge, while charge $\eta$-spin triplet excitations carry charge but no spin, and both spin-singlet and charge $\eta$-spin-singlet ...

We show that a generalized charge SU(2) symmetry of the one-dimensional (1D) Hubbard model in an infinitesimal flux $\phi$ generates half-filling states from metallic states which lead to a finite charge stiffness $D(T)$ at finite temperature $T$, whose $T$ dependence we study. Our results are of general nature for many integrable quantum lattice systems, reveal the microscopic mechanisms behind their exotic $T>0$ transport properties and the interplay with T=0 quantum-phase ...

In this work, we present a proof of the existence of real and ordered solutions to the generalized Bethe Ansatz equations for the one dimensional Hubbard model on a finite lattice, with periodic boundary conditions. The existence of a continuous set of solutions extending from any positive U to the limit of large interaction is also shown. This continuity property, when combined with the proof that the wavefunction obtained with the generalized Bethe Ansatz is normalizable, i...

This work deals with the one-dimensional Hubbard model. It has seven chapters: 1. Introduction; 2. The Hubbard Model; 3. Algebraic Representation for the Hilbert Space of the 1D Hubbard Model; 4. Pseudoparticle Perturbation Theory; 5. Excitations and Finite-Size Effects; 6. Zero-Temperature Transport; 7. Conclusions.

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 hydr...

The repulsive Hubbard model has been immensely useful in understanding strongly correlated electron systems, and serves as the paradigmatic model of the field. Despite its simplicity, it exhibits a strikingly rich phenomenology which is reminiscent of that observed in quantum materials. Nevertheless, much of its phase diagram remains controversial. Here, we review a subset of what is known about the Hubbard model, based on exact results or controlled approximate solutions in ...