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

• Published in: arXiv.org
• Main Authors: Brügger, C, Hofmann, C P, Kämpfer, F, Moser, M, Pepe, M, U -J Wiese
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 11.06.2007
• Subjects: Antiferromagnetism; Electrons; Magnons; Physics - Strongly Correlated Electrons; Wave functions
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.0706.1423

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.