|Ph.D Student||Ehud Altman|
|Subject||Effective Hamiltonians for Cuprate Bosonic Atoms|
|Department||Department of Physics||Supervisor||Full Professor Auerbach Assa|
We reduce models of strongly interacting particles to effective hamiltonians which are more amenable to approximations. In the first part of the thesis we review and further develop the Contractor renormalization method of Morningstar and Weinstein which derives lower energy effective hamiltonians for new degrees of freedom. We use it to reduce the Hubbard model of repulsively interacting electrons, relevant to the cuprate superconductors, to the Plaquette Boson Fermion Model (PBFM). The four bosons (an antiferromagnon triplet and a d-wave hole pair), are defined by the lowest plaquette eigenstates. The pairs and magnons interact repulsively and their hopping parameters are comparable. This explains the rapid destruction of antiferromagnetic order with emergence of superconductivity in the cuprates and validates a key assumption of the projected SO(5) theory. With hole fermions occupying small Fermi pockets and andreev coupled to hole pair bosons, the PBFM yields several testable predictions such as the existence of two energy gaps with opposite doping dependence. In the last part of the thesis we analyze the dynamics of interacting bosons on an optical lattice. We truncate the hilbert space to derive an effective spin-1 hamiltonian. A novel bosonic representation which we develop, leads to a theory of macroscopic quantum dynamics. We find collective oscillations of the superfluid order following non adiabatic changes to the optical lattice parameters and calculate their frequency and damping rate. Some of these oscillations have been observed recently in an experiment. A similar experiment which can directly observe quantum critical dynamics is proposed.