Thermal conductivity and heat diffusion in the two-dimensional Hubbard model

Abstract

We study the electronic thermal conductivity ${\kappa }_{\text{el}}$ and the thermal diffusion constant $D_{\text{Q,el}}$ in the square lattice Hubbard model using the finite-temperature Lanczos method. We exploit the Nernst-Einstein relation for thermal transport and interpret the strong non-monotonous temperature dependence of ${\kappa }_{\text{el}}$ in terms of that of $D_{\text{Q,el}}$ and the electronic specific heat $c_{\text{el}}$. We present also the results for the Heisenberg model on a square lattice and ladder geometries. We study the effects of doping and consider the doped case also with the dynamical mean-field theory. We show that ${\kappa }_{\text{el}}$ is below the corresponding Mott-Ioffe-Regel value in almost all calculated regimes, while the mean free path is typically above or close to lattice spacing. We discuss the opposite effect of quasi-particle renormalization on charge and heat diffusion constants. We calculate the Lorenz ratio and show that it differs from the Sommerfeld value. We discuss our results in relation to experiments on cuprates. Additionally, we calculate the thermal conductivity of overdoped cuprates within the anisotropic marginal Fermi liquid phenomenological approach.

arXiv comment8+5 figures

References in corpus (51)

• Theory of universal incoherent metallic transport
• Saturation of electrical resistivity
• Fermionic transport in a homogeneous Hubbard model: Out-of-equilibrium dynamics with ultracold atoms
• Experiments on Ladders Reveal a Complex Interplay between a Spin-Gapped Normal State and Superconductivity
• Finite temperature Drude weight of the one dimensional spin 1/2 Heisenberg model}
• Bad metallic transport in a cold atom Fermi-Hubbard system
• Energy resolution and discretization artefacts in the numerical renormalization group
• How bad metals turn good: spectroscopic signatures of resilient quasiparticles
• Breakdown of Fermi-liquid theory in a cuprate superconductor
• Anisotropic Scattering and Anomalous Transport in a High Temperature Superconductor
• Subdiffusion and heat transport in a tilted 2D Fermi-Hubbard system
• Spin Transport in a Mott Insulator of Ultracold Fermions
• Heat conduction in low-dimensional quantum magnets
• Thermal transport and phonon hydrodynamics in strontium titanate
• Ground State and Finite Temperature Lanczos Methods
• Asymptotic scaling of the square lattice quantum Heisenberg antiferromagnet
• Non-Fermi liquids and the Wiedemann-Franz law
• Strange metallicity in the doped Hubbard model
• Specific heat of quasi-2D antiferromagnetic Heisenberg models with varying inter-planar couplings
• Determining the Wiedemann-Franz ratio from the thermal Hall conductivity: Application to Cu and YBa_2Cu_3O_6.95
• Magnetism of the N=42 kagome lattice antiferromagnet
• Magnon Heat Transport in doped $\mathrm{L}{\mathrm{a}}_2\mathrm{Cu}{\mathrm{O}}_4$
• Wiedemann-Franz law and Fermi liquids
• Anomalous Thermal Diffusivity in Underdoped YBa${}_2$Cu${}_3$O${}_{6+x}$
• Electro Thermal Transport Coefficients at Finite Frequencies
• Conductivity in the square lattice Hubbard model at high temperatures: importance of vertex corrections
• Correlation between $T_c$ and anisotropic scattering in Tl${}_2$Ba${}_2$CuO${}_{6+\delta }$
• 1/S-expansion study of spin waves in a two-dimensional Heisenberg antiferromagnet
• Thermodynamics of the planar Hubbard model
• Transport and Optical Conductivity in the Hubbard Model: A High-Temperature Expansion Perspective
• Thermodynamics of a bad metal-Mott insulator transition in the presence of frustration
• Violation of Wiedemann-Franz law at the Kondo breakdown quantum critical point
• Charge transport in the Hubbard model at high temperatures: triangular versus square lattice
• Bad-Metallic Behavior of Doped Mott Insulators
• Fermi-liquid behavior and thermal conductivity of ε-iron at Earth's core conditions
• Evidence for a large magnetic heat current in insulating cuprates
• High-temperature superconductors of the family (RE)Ba2Cu3O7-delta and their application (Review Article)
• On the Planckian bound for heat diffusion in insulators
• Absence of a quantum limit to charge diffusion in bad metals
• Tracking anisotropic scattering in overdoped Tl${}_2$Ba${}_2$CuO${}_{6+\delta }$ above 100 K
• Thermal Diffusivity Above Mott-Ioffe-Regel Limit
• Transport properties of the metallic state of overdoped cuprate superconductors from an anisotropic marginal Fermi liquid model
• Hubbard-to-Heisenberg crossover (and efficient computation) of Drude weights at low temperatures
• Two-particle Fermi liquid parameters at the Mott transition: Vertex divergences, Landau parameters, and incoherent response in dynamical mean-field theory
• Holon-Doublon Binding as the Mechanism for the Mott transition
• Spin diffusion of the t-J model
• Consistent description of the metallic phase of overdoped cuprate superconductors as an anisotropic marginal Fermi liquid
• Transport in the 2D Fermi-Hubbard Model: Lessons from Weak Coupling
• Magnon heat transport in a two-dimensional Mott insulator
• Spin diffusion and spin conductivity in the 2d Hubbard model
• Spin Seebeck coefficient and spin-thermal diffusion in the two-dimensional Hubbard model

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