The infinite range Heisenberg model and high temperature superconductivity

Citation

Tahir-Kheli, Jamil (1992) The infinite range Heisenberg model and high temperature superconductivity. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/9JDD-4P11. https://resolver.caltech.edu/CaltechETD:etd-05042006-112846

Abstract

NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.

The thesis deals with the theory of high temperature superconductivity from the standpoint of three-band Hubbard models.

Chapter 1 of the thesis proposes a strongly coupled variational wavefunction that has the three-spin system of an oxygen hole and its two neighboring copper spins in a doublet and the background Cu spins in an eigenstate of the infinite range antiferromagnet. This wavefunction is expected to be a good "zeroth order" wavefunction in the superconducting regime of dopings. The three-spin polaron is stabilized by the hopping terms rather than the copper-oxygen antiferromagnetic coupling Jpd. Considering the effect of the copper-copper antiferromagnetic coupling Jdd, we show that the three-spin polaron cannot be pure Emery (Dg), but must have a non-negligible amount of doublet-u (Du) character for hopping stabilization. Finally, an estimate is made for the magnitude of the attractive coupling of oxygen holes.

Chapter 2 presents an exact solution to a strongly coupled Hamiltonian for the motion of oxygen holes in a 1-D Cu-O lattice. The Hamiltonian separates into two pieces: one for the spin degrees of freedom of the copper and oxygen holes, and the other for the charge degrees of freedom of the oxygen holes. The spinon part becomes the Heisenberg antiferromagnet in 1-D that is soluble by the Bethe Ansatz. The holon piece is also soluble by a Bethe Ansatz with simple algebraic relations for the phase shifts.

Finally, we show that the nearest neighbor Cu-Cu spin correlation increases linearly with doping and becomes positive at x [...] 0.70.

Thesis Files