Statics and dynamics of charge fluctuations in the t-J model

TL;DR

This paper derives and solves the charge vertex equation in the t-J model, revealing that charge screening and fluctuation dynamics are primarily influenced by the no-double-occupancy constraint rather than the exchange interaction J.

Contribution

It provides a leading-order solution for the charge vertex in the t-J model using an 1/N expansion and Hubbard operators, highlighting the weak dependence on J.

Findings

Charge screening is weakly dependent on J.

Charge fluctuation dynamics are mainly governed by the no-double-occupancy constraint.

Calculated charge-related quantities include electron lifetime and charge-charge correlation functions.

Abstract

The equation for the charge vertex $\gamma$ of the $t-J$ model is derived and solved in leading order of an 1/N expansion, working directly in terms of Hubbard operators. Various quantities which depend crucially on $\gamma$ are then calculated, such as the life time and the transport life time of electrons due to a charge coupling to other degrees of freedom and the charge-charge correlation function. Our results show that the static screening of charges and the dynamics of charge fluctuations depend only weakly on $J$ and are mainly determined by the constraint of having no double occupancies of sites.