Cumulant approach to weakly doped antiferromagnets

TL;DR

This paper introduces a cumulant-based method to analyze static and dynamic properties of holes and spins in weakly doped two-dimensional antiferromagnets, revealing strong spin-hole interactions and explaining experimental doping effects.

Contribution

The paper presents a novel cumulant approach to evaluate dispersion relations and ground-state properties, capturing the mutual influence of holes and spin waves in doped antiferromagnets.

Findings

Strong spin-wave and hole coupling suppresses staggered magnetization.

Doping dependence of spin-wave energies explained by the model.

Method accurately derives hole excitation dispersion at half-filling.

Abstract

We present a new approach to static and dynamical properties of holes and spins in weakly doped antiferromagnets in two dimensions. The calculations are based on a recently introduced cumulant approach to ground--state properties of correlated electronic systems. The present method allows to evaluate hole and spin--wave dispersion relations by considering hole or spin excitations of the ground state. Usually, these dispersions are found from time--dependent correlation functions. To demonstrate the ability of the approach we first derive the dispersion relation for the lowest single hole excitation at half--filling. However, the main purpose of this paper is to focus on the mutual influence of mobile holes and spin waves in the weakly doped system. It is shown that low-energy spin excitations strongly admix to the ground--state. The coupling of spin waves and holes leads to a strong suppression of the staggered magnetization which can not be explained by a simple rigid--band picture for the hole quasiparticles. Also the experimentally observed doping dependence of the spin--wave excitation energies can be understood within our formalism.