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The infinite range Heisenberg model and high temperature superconductivity


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.


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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.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Bethe ansatz; cuprates; Heisenberg antiferromagnet; high temperature superconductivity; superconductivity
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Physics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Goddard, William A., III
Thesis Committee:
  • Goddard, William A., III (chair)
  • Goodstein, David L.
  • Cross, Michael Clifford
  • Frautschi, Steven C.
Defense Date:15 May 1992
Non-Caltech Author Email:jamil (AT)
Record Number:CaltechETD:etd-05042006-112846
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:1605
Deposited By: Imported from ETD-db
Deposited On:12 May 2006
Last Modified:21 Dec 2019 04:44

Thesis Files

PDF (Tahir-Kheli_thesis_final.pdf) - Final Version
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