|M.Sc Student||Berg Erez|
|Subject||Effective Hamiltonians for Frustrated Antiferromagnets|
|Department||Department of Physics||Supervisor||Professor Assa Auerbach|
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.