Loading...

Quantum Phase Transition in Kondo-Necklace Model: Concurrence Measure Within Perturbative Continuous Unitary Transformation Formalism

Hemmatiyan, Shayan | 2011

1442 Viewed
  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 41436 (04)
  4. University: Sharif University of Technology
  5. Department: Physics
  6. Advisor(s): Langari, Abdollah
  7. Abstract:
  8. In this thesis, we consider the Kondo-necklace model to investigate the quantum phase transition between the Kondo-singlet and antiferromagnetic phases. There is no exact solution for this model. We would like to study the quantum critical behaviour of this model on one, two and three dimensional spaces in addition to ladder geometry. In this respect, we looked for a proper method which can give us some information for our model on any spaces mentioned above. Therefore, we implemented the perturbation continuous unitary transformation (PCUT) for the Kondo-necklace model. By using this method, we can not only calculate the ground state energy for 1, 2, 3 dimension and n-leg ladder Kondo-necklace model, but also the correlation functions. On the other hand, as a matter of fact, condensed matter physicist are immensely interested in quantum information properties especially quantum entanglement in their models because they can see some exciting properties in quantum entanglement near quantum critical point of several model Hamiltonians. We have obtained the concurrence (as a bipartite measure of entanglement) from the correlation functions which have been obtained via a generating function. We have observed the concurrence has a maximum after the quantum critical point. In addition, the manipulation of concurrence in the presence of simultaneous symmetry breaking gives a singularity in the first derivative of concurrence at the quantum critical point. It justifies that the concurrence can be a good identifier of the quantum critical point in Kondo-necklace model. Finally, we calculate the concurrence for n-leg kondo-necklace model on ladder geometry and figure out that the dimensional cross over appears immediately from a chain to two-leg ladder. In other words, the two leg ladder behaves similar to the two dimensional Kondo-necklace model
  9. Keywords:
  10. Koando-Necklace Model ; Quantum Phase Transition ; Continuous Unitary Transformation ; Concurrence

 Digital Object List

 Bookmark

...see more