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Magnetic interactions between strongly correlated impurities coupled to a sea of conduction electrons is a subject of great interest from both, experimental and theoretical studies. When many magnetic impurities are attached to the same conduction band a rich phase diagram can arise. By one hand the magnetic impurities can be strongly coupled to the spin of the electrons of the conduction band forming a Kondo singlet. By the other, through electron of the conduction band, a spin-spin interaction between the impurities can appears as a consequence the RKKY interaction. A competition between this two singles is expected. For these two effects is important to have a good description of the electrons with energy close to the Fermi level. Systems like the square lattice, with a van-Hove singularity at the middle of the band, or Graphene, with Dirac electrons, or Carbon nanotubes with multiple bands and multiples van Hove singularities need a proper description of the electrons in the lattice Hamiltonian.
In this work we propose a canonical transformation to study problems with several magnetic impurities coupled to arbitrary lattices using DMRG or ECA techniques. We present results of the competition between Kondo effect and RKKY interaction in a multi band system. |
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