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Ferromagnetism in the one-dimensional Kondo lattice: Mean-field approach via Majorana fermion canonical transformation

Journal article
Authors Matteo Bazzanella
Johan Nilsson
Published in Physical Review B. Condensed Matter and Materials Physics
Volume 89
Issue 3
Pages artikel nr 035121
ISSN 1098-0121
Publication year 2014
Published at Department of Physics (GU)
Pages artikel nr 035121
Language en
Links dx.doi.org/10.1103/PhysRevB.89.0351...
Keywords Majorana fermions, kondo lattice, spin-selective kondo insulator, spin liquid
Subject categories Magnetism, Electronic structure

Abstract

Using a canonical transformation, it is possible to faithfully represent the Kondo lattice model in terms of Majorana fermions. Studying this representation, we discovered an exact mapping between the Kondo lattice Hamiltonian and a Hamiltonian describing three spinless fermions interacting on a lattice. This alternative form of the Hamiltonian is suitable for an immediate identification of the competing effects that operate in the Kondo lattice model. In particular, a term describing the double-exchange mechanism appears explicitly in the Hamiltonian. We investigate the effectiveness of this three-fermion representation by performing a zero-temperature mean-field study of the phase diagram at different couplings and fillings for the one-dimensional case, focusing on the appearance of ferromagnetism. The solutions show interesting features that agree in many respects with the known numerical and analytical results. In particular, in the ferromagnetic region connected to the solution at zero electron density, we have a quantitative agreement on the value of the “commensurability parameter” discovered in recent density matrix renormalization group (in one dimension) and dynamical mean-field theory (in infinite dimensions) simulations; furthermore, we provide a theoretical justification for it, identifying a symmetry of the Hamiltonian. This ferromagnetic phase is stabilized by the emergence of a spin-selective Kondo insulator, which is described quite conveniently by the three spinless fermions. We discover, however, that such a phase cannot be the correct description for all the ferromagnetic phases of the one-dimensional Kondo lattice model. We found in fact a different ferromagnetic phase at high filling and low couplings. This phase resembles the Ruderman-Kittel-Kasuya-Yosida (RKKY) ferromagnetic phase existing at vanishing filling, but it incorporates much more of the Kondo effect, making it energetically more favorable than the typical spiral (spin ordered) mean-field ground states. We believe that this second phase represents a prototype for the strange ferromagnetic tongue identified by numerical simulations inside the paramagnetic dome. At the end of the work, we also provide a discussion of possible orders different from the ferromagnetic one. In particular, at half-filling, where we obtain as ground state at high coupling the correct Kondo insulating state.

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