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178 CHAPTER 7. CONCLUSION although the energy gain of the superconducting wavefunction is small, and it is difficult to get a definitive conclusion on the exact nature of the RVB phase. We proposed additionally two other models that might shed light on the presence of orbital currents: (1) We extended first the three-band Hubbard model by considering the additional out-of-plane apical oxygens and the copper d 3z2−r2 orbitals, (2) We considered an additional correlated hopping term in the three-band Hubbard model. In the former model we found interestingly that when the transfer integrals connected to the apical oxygen are slightly enhanced, then strong orbital currents start to develop with an in-plane magnetic moment, in agreement with neutron experimental results. In the latter model, we found that the orbital currents are strongly stabilized when the correlated hopping V 2 ≈ 0.4. The symmetry of the current pattern in this case is θ 2 like. Additionally, we have studied further the orbital current present in the three-band Hubbard model when open boundaries are considered. In this particular case, the flux flowing through the boundary is removed, and the charge current phase is still stabilized. Finally, it has also been argued that holes doped in the antiferromagnetically correlated spin systems induce incommensurate spin correlations in the ground state for the one-band hubbard model and three-band model within the mean-field approximation. Therefore, it would be interesting to compare the energies of these phases with our Jastrow projected wavefunction, and see if these phases are still present.
Bibliography [1] J. G. Bednorz and K. A. Mller. Z. Physik B, 1986. [2] L. Gao, Y. Y. Xue, F. Chen, Q. Xiong, R. L. Meng, D. Ramirez, C. W. Chu, J. H. Eggert, and H. K. Mao. Phys. Rev. B, 1994. [3] N. D. Mermin. Phys. Rev., 176:250, 1968. [4] mark S. Hybertsen and Michael Schlter. Phys. Rev. B, 39(13):9028, 1989. [5] D. S. Dessau, Z.-X. Shen, D. M. King, D. S. Marshall, L. W. Lombardo, P. H. Dickinson, A. G. Loeser, J. DiCarlo, C.-H Park, A. Kapitulnik, and W. E. Spicer. Phys. Rev. Lett., 71(17):2781–2784, Oct 1993. [6] J. G. Tobin, C. G. Olson, C. Gu, J. Z. Liu, F. R. Solal, M. J. Fluss, R. H. Howell, J. C. O’Brien, H. B. Radousky, and P. A. Sterne. Phys. Rev. B, 45(10):5563–5576, Mar 1992. [7]C.M.Varma,S.Schmitt-Rink,andE.Abrahams. Solid State Commun., 62:681, 1987. [8] V.J.Emery.Phys. Rev. Lett., 58:2794, 1987. [9] MarkS.Hybertsen,E.B.Stechel,M.Schluter,andD.R.Jennison.Phys. Rev. B, 41(16):11068, 1990. [10] F. Mila. Phys. Rev. B, 38(16):11358, 1988. [11] J. Zaanen and A. Oleś. Phys. Rev. B, 37:9423, 1988. [12] F. C. Zhang and T. M. Rice. 37:3759, 1988. [13] P. W. Anderson. Mater. Res. Bull., 8:153, 1973. [14] P. W. Anderson. Science, 235:1196, 1987. [15] P. W. Anderson. Science, 235:1196, 1987. [16] Anders W. Sandvik. Physical Review B (Condensed Matter), 56(18):11678– 11690, 1997. 179
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VARIATIONAL STUDY OF STRONGLY CORRE
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12 CONTENTS 3.3.5 Order parameters
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14 CONTENTS
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Page 190 and 191: 190 APPENDIX A. DETERMINANTS AND PF
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