Finite-temperature charge transport in the one-dimensional Hubbard model

Abstract

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 dependence of the conductivity is consistent with a finite dc value and thus with diffusion, despite large finite-size effects. Furthermore, we consider the mass-imbalanced Hubbard model for which the charge Drude weight decays exponentially with system size, as expected for a non-integrable model. We analyze the conductivity and diffusion constant as a function of the mass imbalance and we observe that the conductivity of the lighter component decreases exponentially fast with the mass-imbalance ratio. While in the extreme limit of immobile heavy particles, the Falicov-Kimball model, there is an effective Anderson-localization mechanism leading to a vanishing conductivity of the lighter species, we resolve finite conductivities for an inverse mass ratio of η 0.3.

Thermal Conductivity of the One-Dimensional Fermi-Hubbard Model

“…In ultra-cold quantum gases, relaxation processes play an important role for reaching thermal equilibrium during the state preparation [53,54] [ [56][57][58][59]. We demonstrate that real-space perturbations in the energy density spread ballistically in the 1D FHM at T > 0 while charge diffuses [27,28], providing a route to experimentally observing the qualitative difference between charge and energy dynamics in this model. Definitions.…”

Proposal for measuring the finite-temperature Drude weight of integrable systems

“…3(b) suggests that perturbations in the energy density spread ballistically as expected from theory [16,44] with an exponent of 2, while for the charge dynamics, the exponents are consistently smaller than 2 and the smaller the larger U/t 0 is. We expect that the asymptotic diffusive behavior [47,48] will emerge at times longer than what is accessible in our simulations. Note that one can also study the time dependence of energy and charge density perturbations in quenches that touch both densities [44]: in that case, one can visualize the coexistence of ballistic energy transport with diffusive charge transport in the same timeevolution.…”

Real-time broadening of nonequilibrium density profiles and the role of the specific initial-state realization

“…Thus, we proceed differently and rely on a forward propagation of |ψ(t) in real time. Such a propagation can be done by the use of fourth-order Runge-Kutta [14,30,31] or more sophisticated schemes such as Trotter decompositions or Chebyshev polynomials [43,44]. Here, we use a massively parallelized implementation of a Chebyshev-polynomial algorithm.…”