Spiral phases and two-particle bound states from a systematic low-energy effective theory for magnons, electrons, and holes in an antiferromagnet

TL;DR

This paper develops a low-energy effective theory for doped antiferromagnets to analyze magnon-mediated two-particle bound states, revealing bound states with specific symmetries and insights into ground states.

Contribution

It introduces a systematic low-energy effective theory for doped antiferromagnets and investigates magnon-mediated binding, deriving potentials and solving for bound states with specific symmetries.

Findings

Bound states with $d_{x^2-y^2}$-like symmetry

Bound states with $d_{xy}$-like symmetry

Insights into ground states of lightly doped antiferromagnets

Abstract

We have constructed a systematic low-energy effective theory for hole- and electron-doped antiferromagnets, where holes reside in momentum space pockets centered at $(\pm\frac{\pi}{2a},\pm\frac{\pi}{2a})$ and where electrons live in pockets centered at $(\frac{\pi}{a},0)$ or $(0,\frac{\pi}{a})$. The effective theory is used to investigate the magnon-mediated binding between two holes or two electrons in an otherwise undoped system. We derive the one-magnon exchange potential from the effective theory and then solve the corresponding two-quasiparticle Schr\"odinger equation. As a result, we find bound state wave functions that resemble $d_{x^2-y^2}$-like or $d_{xy}$-like symmetry. We also study possible ground states of lightly doped antiferromagnets.