טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentErez Berg
SubjectEffective Hamiltonians for Frustrated Antiferromagnets
DepartmentDepartment of Physics
Supervisor Full Professor Auerbach Assa


Abstract

Frustrated antiferromagnetic systems are characterized by a macroscopic degeneracy in their classical ground state manifold. As a result, any perturbation added to the Hamiltonian generates a new energy scale in which this degeneracy is lifted. In the case of strong quantum fluctuations new kinds of quantum phases can be stabilized. Even though quantum frustrated antiferromagnets have been studied extensively in recent years, both theoretically and experimentally, no clear understanding of their low temperature behavior has emerged, mainly due to the absence of suitable theoretical tools. The main challenge is to understand the nature of the ground state and the low energy excitations.

In this work, we apply the new Contractor Renormalization (CORE) technique to the spin half Heisenberg model on the highly frustrated checkerboard and pyrochlore lattices. This method allows us to identify low energy local coordinates of the system and to derive effective Hamiltonians for these coordinates. These effective Hamiltonians reproduce the low lying spectrum of the original Hamiltonian.

Both the checkerboard and the pyrochlore appear to have a spin gap to triplet excitations. We found that the ground states are composed of local singlets that break lattice symmetry. Experimental signature of these ground states may be found in corresponding lattice disortions. The low singlet excitations are described by small energy scale Ising-like models, where the pseudospins are defined by spin-singlet doublets  on  tetrahedral blocks.  Our effective Hamiltonians can also be used to predict the thermodynamics and to interpret finite size numerical studies.