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 $\eta \gtrsim 0.25$.

13 pages, 11 figures

References in corpus (21)

• Thermalization and its mechanism for generic isolated quantum systems
• Many body localization and thermalization in quantum statistical mechanics
• Open XXZ spin chain: Nonequilibrium steady state and strict bound on ballistic transport
• Typicality for Generalized Microcanonical Ensembles
• Massive Parallel Quantum Computer Simulator
• Conservation laws, integrability and transport in one-dimensional quantum systems
• Eigenstate thermalization within isolated spin-chain systems
• Eigenstate thermalization hypothesis (ETH) and integrability in quantum spin chains
• A real-time study of diffusive and ballistic transport in spin-1/2 chains using the adaptive time-dependent density matrix renormalization group method
• Diffusive high-temperature transport in the one-dimensional Hubbard model
• Spin Drag and Spin-Charge Separation in Cold Fermi Gases
• Density dynamics in translationally invariant spin-1/2 chains at high temperatures: a current auto-correlation approach to finite time- and length-scales
• Spin and energy currents in integrable and nonintegrable spin-1/2 chains: A typicality approach to real-time autocorrelations
• Local and Quasilocal Conserved Quantities in Integrable Systems
• Coexistence of diffusive and ballistic transport in a simple spin ladder
• Breakdown of the generalized Gibbs ensemble for current-generating quenches
• Transport properties of the one-dimensional Hubbard model at finite temperature
• Spin and thermal conductivity of quantum spin ladders
• Scaling of diffusion constants in the spin-1/2 XX ladder
• Relaxation dynamics of a Fermi gas in an optical superlattice
• Comment on "Anomalous Thermal Conductivity of Frustrated Heisenberg Spin Chains and Ladders"

Cited by in corpus (26)

• Finite-temperature transport in one-dimensional quantum lattice models
• Quasilocal charges in integrable lattice systems
• Super-diffusion in one-dimensional quantum lattice models
• Spin crossovers and superdiffusion in the one-dimensional Hubbard model
• Speck of Chaos
• Real-time broadening of non-equilibrium density profiles and the role of the specific initial-state realization
• Entanglement of midspectrum eigenstates of chaotic many-body systems: Reasons for deviation from random ensembles
• Random State Technology
• Many-Body Localization in System with a Completely Delocalized Single-Particle Spectrum
• Selected applications of typicality to real-time dynamics of quantum many-body systems
• Proposal for measuring the finite-temperature Drude weight of integrable systems
• Hubbard-to-Heisenberg crossover (and efficient computation) of Drude weights at low temperatures
• Accuracy of the microcanonical Lanczos method to compute real-frequency dynamical spectral functions of quantum models at finite temperatures
• Charge stiffness and long-range correlation in the optically induced $\eta$-pairing state of the one-dimensional Hubbard model
• Thermal conductivity of the one-dimensional Fermi-Hubbard model
• Charge diffusion in the one-dimensional Hubbard model
• Tunable transport in the mass-imbalanced Fermi-Hubbard model
• Density dynamics in the mass-imbalanced Hubbard chain
• Typicality-Based Variational Cluster Approach to Thermodynamic Properties of the Hubbard Model
• Spatiotemporal dynamics of classical and quantum density profiles in low-dimensional spin systems
• Two-doublon Bloch oscillations in the mass-imbalanced extended Fermi-Hubbard model
• Nontrivial damping of quantum many-body dynamics
• Infinite temperature spin dynamics in the asymmetric Hatsugai-Kohmoto model
• Anomalous Quantum Relaxation in the Infinite Temperature Hubbard Chain
• Photodynamic melting of phase-reversed charge stripes and enhanced condensation
• Particle pairing causes subdiffusion of heavy particles in the imbalanced Hubbard model