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66 CHAPTER 3. T-J MODEL ON THE TRIANGULAR LATTICE 0.00 -0.02 N=12 e c -0.04 -0.06 -0.08 d + AF / J AF+d + / J AF+d + / J / 1Ls AF+d + / J / 2Ls ED -0.10 1 1.1 1.2 1.3 Electron density n Figure 3.6: Condensation energy per site versus the electron doping for a 12 site cluster for the different variational wavefunctions. We have done exact diagonalization (ED) for a 12 sites cluster with same periodic boundary conditions.
3.4. RESULTS AND DISCUSSION 67 0 -0.02 e c -0.04 -0.06 d + AF / J AF+d + / J AF+d + / J / Ls N=108 -0.08 1 1.1 1.2 1.3 1.4 1.5 Electron density n Figure 3.7: Condensation energy per site e c versus electron doping for the 108 site lattice. We show different wavefunctions and also the best estimate in the literature [82] at half-filling (open diamond). the condensation energy per site (see Fig. 3.7) for different types of instabilities. Very interestingly, the AF/J is even better than a simple d x 2 −y 2 + id xy RVB state. Moreover, the RVB order only weakly increases the condensation energy in presence of the antiferromagnetic background (AF + d + /J). This suggests that superconductivity is only weakly present in the t−J model when n>1which is also confirmed by the measurement of the superconducting gap (see Fig. 3.9). The RV B/J wavefunction, although it allows to recover a very good variational energy at half-filling, is not stabilized in the electron doping side of the phase diagram (see Fig. 3.8). The superconducting order of our best wavefunction is approximately 4 times smaller in amplitude and in range of stability than the d-wave pairing in a 10 × 10 square lattice with the same boundary conditions. For electron doping δ>0.04 we find that the d + BCS pairing symmetry has the same energies as the d − one, and also as the wavefunctions with d x 2 −y 2 and d xy pairings. Very strikingly, the 120 ◦ magnetic order parameter is surviving up to high doping δ =0.4, see Fig. 3.11. Long-range magnetic order at finite doping is potentially caused by a limitation of the VMC method, since it is not possible in
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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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116 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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