The role of the lattice structure in determining the magnon-mediated interactions between charge carriers doped into a magnetically ordered background

TL;DR

This paper investigates how the lattice structure influences magnon-mediated interactions between charge carriers in magnetic backgrounds, revealing limitations of simplified models in capturing complex two-carrier dynamics.

Contribution

The study compares exact spectra of two carriers in complex models and simpler Hamiltonians, showing that simplified models fail to reproduce magnon-mediated interactions.

Findings

Simpler models do not capture magnon-mediated interactions in two-carrier states.

One-particle states are well-described by simpler Hamiltonians.

Results challenge the adequacy of one-band models for cuprate physics.

Abstract

We use two recently proposed methods to calculate exactly the spectrum of two spin-${1\over 2}$ charge carriers moving in a ferromagnetic background, at zero temperature, for three types of models. By comparing the low-energy states in both the one-carrier and the two-carrier sectors, we analyze whether complex models with multiple sublattices can be accurately described by simpler Hamiltonians, such as one-band models. We find that while this is possible in the one-particle sector, the magnon-mediated interactions which are key to properly describe the two-carrier states of the complex model are not reproduced by the simpler models. We argue that this is true not just for ferromagnetic, but also for antiferromagnetic backgrounds. Our results question the ability of simple one-band models to accurately describe the low-energy physics of cuprate layers.