Transport of Strongly Correlated Electrons

Lectures deal with the theory of electronic transport, in particular with the electrical conductivity, in systems dominated by strong electron-electron repulsion. The concept of charge stiffness is introduced to distinguish conductors and insulators at T=0, but as well usual resistors, possible ideal conductors and ideal insulators at finite temperature. It is shown that the latter singular transport appears in many integrable systems of interacting fermions, the evidence coming from the relation with level dynamics, from the existence of conserved quantities as well as from numerical studies and exact results. Then, exact duagonalization approaches for the calculation of static and dynamical quantities in small correlated systems are described, with the emphasis on the finite-temperature Lanczos method applicable to transport quantities. Finally, anomalous dynamical conductivity within the planar single-band model is discussed in relation with experiments on cuprates.