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

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.

34 pages, 1 figure

References in corpus (9)

• Perturbative nuclear physics
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• Constraint Effective Potential of the Staggered Magnetization in an Antiferromagnet
• Homogeneous versus Spiral Phases of Hole-doped Antiferromagnets: A Systematic Effective Field Theory Investigation
• Systematic Low-Energy Effective Field Theory for Electron-Doped Antiferromagnets
• Loop-Cluster Simulation of the $t$-$J$ Model on the Honeycomb Lattice
• Ferromagnetic spin-polaron on complex lattices
• Systematic Effective Field Theory Investigation of Spiral Phases in Hole-Doped Antiferromagnets on the Honeycomb Lattice
• Hund's rule and metallic ferromagnetism

Cited by in corpus (8)

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• Low-Temperature Properties of Two-Dimensional Ideal Ferromagnets
• Thermodynamics of Two-Dimensional Ideal Ferromagnets - Three-Loop Analysis
• Low-Temperature Properties of Ferromagnetic Spin Chains in a Magnetic Field
• Thermodynamics of Ferromagnetic Spin Chains in a Magnetic Field: Impact of the Spin-Wave Interaction
• Systematic Effective Field Theory Analysis of the D=2+1 Quantum XY Model at Low Temperatures
• Property $(TT)$ modulo $T$ and homomorphism superrigidity into mapping class groups
• Thermodynamics of the $d$=3+1 Quantum XY Model