Derivation of the t-J model for finite doping

TL;DR

This paper extends the derivation of the t-J model to finite doping levels in strongly correlated fermionic systems, using advanced transformation techniques to determine the model's parameters beyond half-filling.

Contribution

It introduces a novel derivation method for the t-J model at finite doping using self-similar continuous unitary transformations and normal-ordering relative to a doped reference.

Findings

Coupling constants for the t-J model at finite doping are calculated.

The applicability range of the t-J model is characterized as a function of doping and interaction parameters.

The derivation extends the theoretical understanding of doped Mott insulators.

Abstract

Mapping complex problems to simpler effective models is a key tool in theoretical physics. One important example in the realm of strongly correlated fermionic systems is the mapping of the Hubbard model to a t-J model which is appropriate for the treatment of doped Mott insulators. Charge fluctuations across the charge gap are eliminated. So far the derivation of the t-J model is only known at half-filling or in its immediate vicinity. Here we present the necessary conceptual advancement to treat finite doping. The results for the ensuing coupling constants are presented. Technically, the extended derivation relies on self-similar continuous unitary transformations (sCUT) and normal-ordering relative to a doped reference ensemble. The range of applicability of the derivation of t-J model is determined as function of the doping $\delta$ and the ratio bandwidth W over interaction U.