Conductivity and Hall effect in the two-dimensional Hubbard model

Abstract

A path-integral field-theoretic derivation of electromagnetic linear response for the two-dimensional Hubbard model is given. We find, remarkably, that changes in the Fermi-surface topology associated with incommensurate planar spin-density-wave saddle points induce a change in sign of the Hall coefficient at dopings ${\mathrm{\ensuremath{\delta}}}_{\mathit{H}}$=0.02--0.5 for U/t=2--10. The change in sign is not affected by short-range magnetic domains. We delinate from first principles an anomalous temperature dependence of the Hall carrier density at dopings close to ${\mathrm{\ensuremath{\delta}}}_{\mathit{H}}$. An additional anisotropic component to the usual dc conductivity is nonvanishing for certain types of spirals. The paper extends the Bloch-Boltzmann theory to the case of untraditional Fermi liquids where the damping of the quasiparticles is \ensuremath{\Gamma}(\ensuremath{\epsilon})\ensuremath{\sim}max(${\mathit{k}}_{\mathit{B}}$T,\ensuremath{\epsilon}).