Hall number, optical sum rule and carrier density for the t-t'-J model

Abstract

We revisit the relationship between three classical measures of particle number, namely, the chemical doping x, the Hall number x_Hall, and the particle number inferred from the optical sum rule x_opt. We study the t-t'-J model of correlations on a square lattice, as a minimal model for high T_c systems, using numerical methods to evaluate the low temperature Kubo conductivities. These measures disagree significantly in this type of system, owing to Mott Hubbard correlations. The Hall constant has a complex behavior with several changes of sign as a function of filling x, depending on the model parameters. Thus, x_Hall depends sensitively on t' and J due to a kind of quantum interference.