The Hall Number, Optical Sum Rule and Carrier Density for the $t$-$t'$-$J$ model

TL;DR

This paper investigates the discrepancies among different measures of particle density in the $t$-$t'$-$J$ model, revealing complex behaviors influenced by correlations and model parameters, which are relevant for understanding high-temperature superconductors.

Contribution

The study provides a detailed numerical analysis of how the Hall number, optical sum rule, and chemical doping differ in the $t$-$t'$-$J$ model, highlighting the effects of correlations and parameter sensitivity.

Findings

Hall constant exhibits multiple sign changes with filling.

Significant disagreement among particle number measures due to correlations.

Hall number's dependence on $t'$ and $J$ shows quantum interference effects.

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 conductivites. 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 upon the model parameters. Thus $x_{hall}$ depends sensitively on $t'$ and $J$, due to a kind of quantum interference.