Loading...

Fermionic Approach To The One Dimensional Kondo Necklace Model

Arab, Arian |

1193 Viewed
  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 44448 (04)
  4. University: Sharif University of Technology
  5. Department: Physics
  6. Advisor(s): Langari, Abdollah
  7. Abstract:
  8. Strongly correlated materials are kind of materials in which novel electric and magnetic properties will appear as a result of strong correlations among their electrons like “heavy fermion materials”. Kondo lattice model is a model to describe heavy fermion materials. If we are merely interested in the magnetic properties of heavy fermions we can replace the Kondo lattice Model with the simpler model called the Kondo-necklace model which consists of the interactions only among the spins of the itinerant (conduction) and localized electrons (magnetic impurities) and also the interactions between the spins of the itinerant electrons. In this thesis we investigate the properties of the one dimensional Kondo-necklace model in the weak coupling regime (where the interaction among itinerant and localized electrons (J) is weaker than the interactions between itinerant electrons (t)). If the interaction between itinerant and localized electrons is completely zero the model is exactly solvable by a Jordan-Wigner transformation to free fermions. Now suppose that J is much smaller than t, therefore, we can treat J as a perturbation and study the system perturbatively. First, we present a review on Jordan-Wigner transformation to dimensions higher than one. In chapter 3 we investigate these transformations in two dimension and by which we can calculate the ground and first excited state energy of the two dimensional XX model. In chapter 4 we consider these transformations for the two-Leg ladder system which geometrically is very similar to the one dimensional Kondo-necklace Model. By applying the extended Jordan-Wigner transformations to the two-leg ladder the system is transformed to a spin-less fermionic system; however, the Hamiltonian is not free and consists of the interaction terms of four and six fermion operators. So, we can’t diagonalize this Hamiltonian by merely a simple rotation. We need to find a way to converts this Hamiltonian to a free fermion system. In this respcet, we apply the mean-filed approximation. In chapter 5 we use the same method to diagonalize the one dimensional Kondo-necklace model. It is shown that the model in the mean-filed approximation is always gapped for both regimes of the interactions (the weak and strong regimes). Thus, there is no quantum phase transition in one dimension. The problem which appears in the mean-field approximation is that if we solve the Hamiltonian in the extreme limit of the weak coupling there is still a gap in the system (while we know that the XY model is gapless). Although the gap is very small in value compared to the value of the interaction among the itinerant electrons, it is still non-zero. This controversy is the outcome of the mean-filed approximation. In the strong coupling regime, we obtain very good result where the system is gapped and the value of gap is accurate compared with numerical results.
  9. Keywords:
  10. Koando-Necklace Model ; Magnetic Anisotropic ; Quantum Phase Transition ; Jordan-Wigner Transformations ; Mean Field Approximation

 Digital Object List