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Numerical Study of Anisotropic Ferrimagnetic Chain and Ladder with Density Matrix Renormalization Group Method

Asadzadeh, Mohammad Zhian | 2009

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 39665 (04)
  4. University: Sharif University of Technology
  5. Department: Physics
  6. Advisor(s): Langari, Abdollah
  7. Abstract:
  8. According to Haldane Conjecture Antiferromagnetic Heisenberg Spin Chain with integer spin has an energy gap, and exponential decay of correlation functions , while half integer spin chains are gapless with algebraic decay of correlation functions. A spin chain with two types of spins and Heisenberg interaction shows a mixture of both types of behavior. A ferrimagnet which is composed of two spins (S, s) has two bands of energy, the lower band is gapless and ferromagnetic property while the upper one is gapful with antiferromagnetic behavior. In the present work we have studied the anisotropic ferrimagnet in the presence of a transverse magnetic field. We have shown that the spin wave theory is applicable for certain amounts of magnetic field and can not be applied for the whole range of magnetic field. Later we have implemented the Density Matrix Renormalization Group (DMRG) method to compute the ground state and its magnetic property for the whole range of magnetic field. We have shown that the magnetization in the direction of magnetic field in the presence of transverse magnetic field has two plateaus at 1/2 and 3/2 values. In the region between the two plateaus the system is gapless and the ground state will be degenerate while the staggered magnetization in y direction has a non zero amount where we call it a spin-flop phase. We have also found the amount of critical fields for different values of anisotropies. Then, we have studied the properties of ferrimagnetic ladder which is a result of interaction between two chains. In this study the behavior of the system is similar to a chain but with different amounts of critical fields. We have also calculated the effective Hamiltonian for the strong coupling limit on the rungs. In the ferromagnetic strong coupling limit, the effective hamiltonian is the anisotropic antiferromagnetic Spin 3/2 chain in a transverse magnetic field and in antiferromagnetic strong coupling limit, the effective Hamiltonian is an anisotropic ferromagnetic Spin 1/2 chain in a transverse magnetic field. The magnetic properties of the ladder in the strong coupling limit can be explained with the effective Hamiltonians.

  9. Keywords:
  10. Ferrimagnetic ; Spin Wave Theory ; Band Gap ; Density Matrix Renormalization Group ; Staggered Magnetization

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