Transport of Strongly Correlated Electrons

TL;DR

This paper explores the theory of electronic transport in strongly correlated systems, introducing charge stiffness to distinguish different conductors and insulators, and discusses exact methods and experimental relevance in cuprates.

Contribution

It provides a comprehensive overview of transport phenomena in strongly correlated electrons, including the concept of charge stiffness and exact numerical approaches like the finite-temperature Lanczos method.

Findings

Charge stiffness differentiates conductors and insulators at T=0.

Integrable systems exhibit singular transport properties.

Exact diagonalization methods are effective for small correlated systems.

Abstract

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.