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174 CHAPTER 6. ORBITAL CURRENTS IN THE CUPRATES metry is θ 2 like, and when the hopping signs lead to 4 triangles with positive hopping transfer, the orbital current symmetry is θ 1 like. Current-current correlations measured in the corresponding free Fermi sea wavefunction show that short-range correlations with the respective symmetry are present with corresponding θ 1,2 for these two particular choices of the hopping signs. Nevertheless, these choices of the transfer integrals are arbitrary and do no correspond to the real physical model, which is expected to describe the cuprates. Applying the Variational Monte Carlo method, we found in our best variational Ansatz the presence of small currents for doping close to x =0.08. The symmetry of the currents measured in the projected wavefunction consists of lines of currents, as in the θ 2 phase, but with reversed diagonal currents. We get a net macroscopic current running through the periodic boundary of the lattice, which is clearly forbidden in the thermodynamic limit and suggests that the presence of currents at the variational level might be an artefact. On the other hand, the variational parameters of the variational function are exactly those of the θ 2 phase. The other competing instabilities are the spin-density wave and the resonating valence bond wavefunctions. Antiferromagnetism is found to be stable for x =[0., 0.11], and the Néel magnetism is reduced at half-filling down to 68% of the classical value by the quantum fluctuations. When the doping is close to 0.25%, we find superconductivity with a d-wave like symmetry, 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 integral connected to the apical oxygen are slightly enhanced, then strong orbital currents start to develop with an in-plane magnetic moment, in agreements 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. As an outlook, we would suggest to study further the orbital current present in the three-band Hubbard model when open boundaries are considered. In this particular case, the flux running through the boundary would at least be removed, and the stability of the charge current phase could be better studied. 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- and three-band Hubbard models within mean-field approximations. Therefore, it would be interesting to compare the energies of these phases with our Jastrow projected wavefunction, and see if these latter phases are still present.
Chapter 7 Conclusion For the square lattice, both the variational Monte Carlo method (VMC) [32, 18, 19, 21] and mean-field (MF) theories [20] were successful to find a d-wave superconducting phase that is in good agreement with experimental data. Nevertheless, not so many variational Monte Carlo data exist for other geometries, that might be able to describe well the magnetic and superconducting instabilities in other compounds, like in the cobaltites or in the graphene. Moreover, since the discovery of the high temperature superconductors, one of the leading issue is the origin of the pseudo gap phase which exists in the the low hole doping side (underdoped region) of the phase diagram. No present theory was yet able to catch all the features of the pseudo-gap phase of the cuprates. In the present dissertation, progress has been achieved in these directions. Recent data obtained in the cobaltite compound Na x CoO 2 .yH 2 O showed that superconductivity is obtained by cooling the compound below T =4K [74] and for electron doping between 1/4
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VARIATIONAL STUDY OF STRONGLY CORRE
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4 Abstract
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8 Acknowledgments check that our di
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10 Acknowledgments
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12 CONTENTS 3.3.5 Order parameters
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14 CONTENTS
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16 CHAPTER 1. INTRODUCTION c Ba 2+
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18 CHAPTER 1. INTRODUCTION the CuO
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20 CHAPTER 1. INTRODUCTION local Co
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24 CHAPTER 1. INTRODUCTION (Haldane
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30 CHAPTER 1. INTRODUCTION • In C
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32 CHAPTER 2. NUMERICAL METHODS The
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52 CHAPTER 3. T-J MODEL ON THE TRIA
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112 CHAPTER 5. THE FLUX PHASE FOR T
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Page 180 and 181: 180 BIBLIOGRAPHY [17] E. Dagotto. R
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Page 184 and 185: 184 BIBLIOGRAPHY [98] M. Posternak,
Page 186 and 187: 186 BIBLIOGRAPHY [136] B. Fauqué,
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Page 190 and 191: 190 APPENDIX A. DETERMINANTS AND PF
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Page 198 and 199: Education • Reviewer activity at
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