Microscopic Model versus Systematic Low-Energy Effective Field Theory for a Doped Quantum Ferromagnet

TL;DR

This paper compares a microscopic model and a systematic low-energy effective field theory for a doped quantum ferromagnet, demonstrating exact analytical matching and validating the effective theory's predictive power beyond perturbation theory.

Contribution

It provides an exact analytical comparison between microscopic and effective theories for a doped quantum ferromagnet, confirming the effective theory's accuracy and extending its validation beyond perturbative regimes.

Findings

Exact determination of low-energy parameters by matching theories

Effective theory describes behavior at half-filling and with holes accurately

Effective theory remains valid beyond perturbation theory for weakly bound states

Abstract

We consider a microscopic model for a doped quantum ferromagnet as a test case for the systematic low-energy effective field theory for magnons and holes, which is constructed in complete analogy to the case of quantum antiferromagnets. In contrast to antiferromagnets, for which the effective field theory approach can be tested only numerically, in the ferromagnetic case both the microscopic and the effective theory can be solved analytically. In this way the low-energy parameters of the effective theory are determined exactly by matching to the underlying microscopic model. The low-energy behavior at half-filling as well as in the single- and two-hole sectors is described exactly by the systematic low-energy effective field theory. In particular, for weakly bound two-hole states the effective field theory even works beyond perturbation theory. This lends strong support to the quantitative success of the systematic low-energy effective field theory method not only in the ferromagnetic but also in the physically most interesting antiferromagnetic case.