Large-N expansion based on the Hubbard-operator path integral representation and its application to the $t-J$ model

TL;DR

This paper develops a large-N expansion method for the $t-J$ model using Hubbard-operator path integrals, enabling calculation of correlation functions and comparison with existing techniques.

Contribution

Introduces a novel large-N expansion framework based on Hubbard-operator path integrals with diagrammatic rules for the $t-J$ model.

Findings

Calculated the renormalized $O(1/N)$ boson propagator for J=0

Derived spin-spin and charge-charge correlation functions at leading order 1/N

Compared results with existing literature to validate the approach

Abstract

In the present work we have developed a large-N expansion for the $t-J$ model based on the path integral formulation for Hubbard-operators. Our large-N expansion formulation contains diagrammatic rules, in which the propagators and vertex are written in term of Hubbard operators. Using our large-N formulation we have calculated, for J=0, the renormalized $O(1/N)$ boson propagator. We also have calculated the spin-spin and charge-charge correlation functions to leading order 1/N. We have compared our diagram technique and results with the existing ones in the literature.