Transport and optical conductivity in the Hubbard model: A hightemperature expansion perspective
Abstract
We derive analytical expressions for the spectral moments of the dynamical response functions of the Hubbard model using the hightemperature series expansion. We consider generic dimension d as well as the infinited limit, arbitrary electron density n , and both finite and infinite repulsion U . We use momentreconstruction methods to obtain the oneelectron spectral function, the selfenergy, and the optical conductivity. They are all smooth functions at high temperature and, at large U , they are featureless with characteristic widths of the order of the lattice hopping parameter t . In the infinited limit, we compare the series expansion results with accurate numerical renormalization group and interaction expansion quantum Monte Carlo results. We find excellent agreement down to surprisingly low temperatures, throughout most of the badmetal regime, which applies for T ≳(1 n )D , the BrinkmanRice scale. The resistivity increases linearly in T at high temperature without saturation. This results from the 1 /T behavior of the compressibility or kinetic energy, which play the role of the effective carrier number. In contrast, the scattering time (or diffusion constant) saturates at high T . We find that σ (n ,T )≈(1 n )σ (n =0 ,T ) to a very good approximation for all n , with σ (n =0 ,T )∝t /T at high temperatures. The saturation at small n occurs due to a compensation between the density dependence of the effective number of carriers and that of the scattering time. The T dependence of the resistivity displays a kneelike feature which signals a crossover to the intermediatetemperature regime where the diffusion constant (or scattering time) starts increasing with decreasing T . At high temperatures, the thermopower obeys the Heikes formula, while the WiedemannFranz law is violated with the Lorenz number vanishing as 1 /T^{2} . The relevance of our calculations to experiments probing hightemperature transport in materials with strong electronic correlations or ultracold atomic gases in an optical lattice is briefly discussed.
 Publication:

Physical Review B
 Pub Date:
 December 2016
 DOI:
 10.1103/PhysRevB.94.235115
 arXiv:
 arXiv:1608.01600
 Bibcode:
 2016PhRvB..94w5115P
 Keywords:

 Condensed Matter  Strongly Correlated Electrons
 EPrint:
 38 pages, 16 figures