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

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. 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 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 DMRG (in one dimension) and DMFT (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 that is described quite conveniently by the three spinless fermions. We discovered also a different ferromagnetic phase at high filling and low couplings. This phase resembles the 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.

21 pages, 10 figures

References in corpus (11)

• Fermi-liquid instabilities at magnetic quantum phase transitions
• Fractionalized Fermi liquids
• Spin-Orbital Separation in the quasi 1D Mott-insulator Sr2CuO3
• Unconventional Superconductivity from Local Spin Fluctuations in the Kondo Lattice
• Impurity Entanglement Entropy and the Kondo Screening Cloud
• Variational Monte Carlo approach to the two-dimensional Kondo lattice model
• Ferromagnetic state in the one-dimensional Kondo lattice model
• Impurity entanglement entropy in Kondo systems from conformal field theory
• Canonical representation for electrons and its application to the Hubbard model
• Faithful fermionic representations of the Kondo lattice model
• Majorana fermion description of the Kondo lattice: Variational and Path integral approach