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78 CHAPTER 3. T-J MODEL ON THE TRIANGULAR LATTICE Order parameter (a.u.) 1 0.5 F SDW SC 120˚ SC 0 0.2 0.4 0.6 0.8 1 1.2 1.4 electron density n t
3.4. RESULTS AND DISCUSSION 79 the doped system. On the electron side, mean-field theories would have suggested that the long-range magnetic order state undergoes a first order phase transition [78] into a uniform d + superconducting state at δ ≈ 3% for values of J similar to those considered here. A rationalization of these results would be that the frustration of the lattice, which was from the start the motivation of RVB as a competing state, disfavors magnetic order. Our results, where the Gutzwiller projection is treated exactly within the residual error bars due to the statistics, are in clear disagreement with this mean-field theory. In contrast with the meanfield result, magnetism is dominant and the superconducting order is not favored on the electronic side. In addition, the t−J model on the triangular lattice was expected to have a strong and large RVB instability, since the coordination number is higher than on most of the other lattices, and naively we would expect this to provide an easy way to form singlets. In this chapter we show that it is not the case: for electron doping the system is magnetic, and for hole doping the system is superconducting, but the range of superconductivity is not very large (δ 0.16. We thus confirm that the previous results are not an artefact of their restricted variational subspace, and find an acceptable agreement for the phase diagram. However we emphasize the presence of the spin-density wave wavefunction that was not considered in the mentioned work and implies a small reduction of the superconductivity range. Our calculation thus clearly prompts for a reexaminations of the arguments on the nature of superconductivity in a frustrated lattice. Clearly the non-collinear nature of the order parameter helps making the AF order much more stable to electron doping than initially anticipated. Understanding such issues is of course a very crucial and challenging question. Moreover, on the triangular lattice, no significant enhanced cooperative effect between magnetism and superconductivity seems to be observed: the electron doped side has a magnetic signature, and the hole doped side a superconducting one, but the two orders seem to exclude each other as much as they can, in contrast to what happens for the square lattice. Even in the parts of the phase diagram where coexistence is observed, coexistence
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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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18 CHAPTER 1. INTRODUCTION the CuO
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20 CHAPTER 1. INTRODUCTION local Co
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22 CHAPTER 1. INTRODUCTION that the
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24 CHAPTER 1. INTRODUCTION (Haldane
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26 CHAPTER 1. INTRODUCTION This can
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128 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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