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68 CHAPTER 3. T-J MODEL ON THE TRIANGULAR LATTICE 0.00 -0.02 e c -0.04 -0.06 d + RVB AF/J AF+RVB/J -0.08 0.0 0.1 0.2 electron doping δ 0.3 0.4 Figure 3.8: Condensation energy per site e c versus electron doping for the 96 site lattice. We compare the energy of the RV B wavefunction to the energy of the magnetic AF/J wavefunction. our calculation to model wavefunction with a finite correlation length, i.e. short range 120 ◦ magnetic order. In our calculation, we can either totally suppress the long-range 120 ◦ and get back to the Gutzwiller wavefunction, or use the long-range 120 ◦ magnetic order that is highly stabilized by the potential energy. No intermediate scenario, such as incommensurate structures, is yet available in our calculations, but one can only expect the optimization of the magnetic structure to increase the region of stability for magnetism. We interpret this finding as an indication that the hole motion is not drastically modified by the presence of the non-collinear magnetic structure, so that short range magnetic correlations will survive up to high electron doping. For the t−J z model on the square lattice, it is commonly understood that the Ising Néel order is not surviving high doping because of its costs in kinetic energy: whenever a hole wants to move in an antiferromagnetic spin background, it generates a ferromagnetic cloud. Therefore, good kinetic energies and Néel Ising order are not compatible. In our case, the 3-sublattice order imposes no such constraint on the kinetic energy of the holes, because of the 120 ◦ structure. This can be seen in our wavefunction energies: the potential energy is improved when starting from the Gutzwiller wavefunction and adding 120 ◦ correlations, but the kinetic energy is unchanged. Our best wavefunction has a better potential energy than the Gutzwiller wavefunction (and also than the different CFP wavefunction), but it
3.4. RESULTS AND DISCUSSION 69 0.04 our best wf d + square lattice d x 2 -y 2 N=108 0.04 0.03 0.03 ∆ 0.02 0.02 0.01 0.01 0 0.6 0.8 1 1 1.2 1.4 0 Electron density n Figure 3.9: Superconducting order parameter ∆, obtained by the long-range correlations of the pairing operator (see equation (2.69)), for a 108 site triangular cluster in our best wavefunction (full triangles), in the d + wavefunction (open squares). For comparison we show the amplitude of the d-wave gap in a 10 × 10 square lattice (dashed line).
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VARIATIONAL STUDY OF STRONGLY CORRE
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4 Abstract
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6 Version abrégée
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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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118 CHAPTER 5. THE FLUX PHASE FOR T
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134 CHAPTER 6. ORBITAL CURRENTS IN
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176 CHAPTER 7. CONCLUSION is the st
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178 CHAPTER 7. CONCLUSION although
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180 BIBLIOGRAPHY [17] E. Dagotto. R
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182 BIBLIOGRAPHY [59] F. F. Assad.
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184 BIBLIOGRAPHY [98] M. Posternak,
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186 BIBLIOGRAPHY [136] B. Fauqué,
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188 BIBLIOGRAPHY
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190 APPENDIX A. DETERMINANTS AND PF
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192 APPENDIX B. A PAIR OF PARTICLES
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Education • Reviewer activity at
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2. Model of strongly correlated ele
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List of publications 1. Ising Trans
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Schools, workshops and conferences
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