QuasiHole Properties in TwoDimensional Strongly Correlated Systems
Abstract
The Hubbard and tJ models are widely believed to hold the key to understanding the hightemperature superconductors. This thesis studies the effects of small doping in these models, largely by numerical means. The main results are the following. Chapter 2 uses the Hartree approximation to examine the stability of bag solutions of the twodimensional, oneband Hubbard model, at intermediate values of the on site electron interaction, U, with nearestneighbour (NN, t) and nextnearestneighbour (NNN, t^' ) hopping terms. For U = 3t, even weak NNN hopping destabilizes the polarons. Thus Hartree theory suggests a constraint on spinbag theory: the NNN hopping integral must be small unless both U is moderately large and t ^' > 0. The effect of NNN hopping is also investigated in the tJ model using exact diagonalization. Results for the phase diagram and the band structure are presented. Chapter 3 investigates the tJ model and its variants using the string and hopping bases. For the string basis, states to order t^{10} are treated exactly, so that the Green function is obtained to order t^{20}; the tree approximation is used for the remainder. The hopping basis, which relaxes constraints imposed in the string basis, contains all states generated by up to 8 hops. Properties studied include the groundstate energy, the effective mass, the bandwidth, the spectral function, the self energy, and the density of states. The Ising limit of the tJ model is treated well by the string basis, but the Heisenberg limit J_ = J_ {z} requires the hopping basis, which gives apparently good results for all J > 0.1t. Chapter 4 presents accurate numerical results for lowlying one and twohole states in the tJ model on a 4 x 4 lattice. A previously unremarked degeneracy of vec k = (0,0) S = 1/2 and S = 3/2 onehole levels at t/J = 1/2 is noted; the degeneracy is consistent with a recent analytical result. For small t/J, the S = 1/2 onehole and S = 0 twohole bandwidths on the 4 x 4 lattice are W_{h} = 1.1904457(1)t and W_{hh} = 2.575(4)t^{2}/J respectively. As a measure of finitesize effects we determined the rms holehole separation in the twohole ground states; we find evidence of important finitesize effects for t/J > 1, for which the rms holehole separation is clearly constrained by the 4 x 4 lattice. Intermediate t/J hole separations and binding energies for 0.3 < t/J < 1 however scale approximately as powers of t/J, and can be used to give bulklimit estimates at the more physical t/J = 3.
 Publication:

Ph.D. Thesis
 Pub Date:
 1991
 Bibcode:
 1991PhDT.......275M
 Keywords:

 SUPERCONDUCTORS;
 Physics: Condensed Matter