Polaron states in a CuO chain

TL;DR

This paper models polaron states in a one-dimensional CuO chain, analyzing hole propagation and spin interactions using Green's functions and the self-consistent Born approximation, providing analytical insights into the polaron formation.

Contribution

It introduces a novel one-dimensional CuO chain model and applies an analytical Green's function approach with the self-consistent Born approximation to study polaron states.

Findings

Analytical solution for hole propagation in the CuO chain.

Validation of numerical integration against the analytical solution.

Insights into spin-flip processes affecting polaron formation.

Abstract

We introduce a one-dimensional model for a CuO chain, with holes and $S=1/2$ spins localized in $3d_{x^2-y^2}$ orbitals, and $p_\sigma$ oxygen orbitals without holes in the ground state. We consider a single hole doped at an oxygen site and study its propagation by spin-flip processes. We develop the Green's function method and treat the hole-spin coupling in the self-consistent Born approximation, similar to that successfully used to study polarons in the regular $t$-$J$ model. We present an analytical solution of the problem and investigate whether the numerical integration is a good approximation to this solution.