pdf, 9 MiB - Infoscience - EPFL

More documents

Recommendations

Info

162 CHAPTER 6. ORBITAL CURRENTS IN THE CUPRATES the simulations with periodic boundary conditions. We emphasize that no condition is present at the variational level that would ensure the current conservations in the variational wavefunction which is proposed as Ansatz for the three-band Hubbard model. Finally, we conclude that the JA/FLUX wavefunction is stabilized also in the case when it cannot have a non-physical flux through the boundary. Nevertheless, the open boundary conditions are also expected to introduce severe finite-size effects, that could also stabilize non-physical phases. 6.10.3 Magnetism and superconductivity According to previous VMC evaluations for the U d = ∞ three-band Hubbard model [140], the antiferromagnetic region extends up to 50% hole doping and the d-wave superconducting phase exists only in the infinitesimally small region near the boundary of the antiferromagnetic phase. Thus, previous VMC results concluded that the chance for d-wave superconductivity is small in the threeband Hubbard model. It was concluded that the parameters of the Hubbard Hamiltonian should be tuned such that the anfiferromagnetic phase shrinks to a smaller range of doping. We propose to study in this section the stabilization of the RVB and magnetic phase with our Jastrow wavefunction, which is expected to treat correctly the correlations. Therefore, besides the orbital current instabilities, we considered also the possibility for Néel magnetic long-range order and superconductivity. We considered as a first approximation only the Q =(π, π) pitch vector for the spin density wave. We would although expect that the pitch vector is doping dependent. This issue was addressed for the three-band Hubbard model in Ref. [59]. The possibility for stripes was also considered by variational calculations [139]. In our work, we expect that the long-range correlations contained in the Jastrow factor will allow a correct treatment of the spin √ correlations. We find indeed that the magnetic order parameter M = lim r→∞ 〈S z i Si+ z 〉) is for our best variational wavefunction 66% of the classical value (see Table 6.2). Using this wavefunction as a guiding function for the fixed node calculations, we find a slightly higher magnetic order with 69%. This value can be compared with the 60% obtained by quantum Monte Carlo in the one-band Heisenberg model. However, in the three-band Hubbard model, the magnetic instability is strongly dependent on the oxygen-oxygen hopping integral t pp . Since this hopping frustrates the geometry, we find that the magnetic order is destroyed when t pp ≈ 2eV . Nevertheless, the magnetic instability is overestimated when compared to the cuprates phase diagram where it vanishes for a small hole doping of approximately x = 2%. The spin density wave is however very likely to be stabilized in variational calculations, since the alternating magnetization allow to avoid double occupancy in the uncorrelated part of the wavefunction. The presence of magnetic order obviously costs kinetic energy, but it it does a better job than a
6.10. VMC ON LARGE LATTICES 163 M=()0.5 0.2 108 192 300 sites sites sites 0.0 -0.2 0.0 hole doping n h 0.2 0.4 √ Figure 6.18: Magnetic order parameter M = lim r→∞ 〈S z i Si+ z 〉) versus the hole doping. The saturated value for the magnetic order parameter is M =0.5. pure local gutzwiller projection, which kills very strongly the kinetic energy. Another way to reduce the double occupancy is done by the resonating valence bond instability, which optimizes both the double occupancy and the kinetic energy. We show in Fig. 6.14 the energy gains of the SDW and RVB instabilities when no projection are present. The two instabilities cross at around x ≈ 20% doping. However, the correlated part of the wavefunction plays a drastic role and clearly needs to be considered. Very interestingly, we find that the symmetry of the pairing ∆ ij is, in the real space representation of the three-band Hubbard model, not restricted to nearest neighbor copper and oxygen sites. Indeed, no energy optimization can be obtained when the pairing is restricted to oxygen-oxygen and copper-oxygen bonds. This can be understood in terms of the Zhang-Rice mapping of the three-band Hubbard model to the one band t−J model. In the frame of this theory, the particles of the t−J model are equivalent to a local copper-oxygen d ↑ (p x↓ − p −x↓ + p y↓ − p −y↓ ) singlet in the three-band language. It was very strongly established that a d-wave RVB instability is present in the t−J model [19, 144, 24, 129], but it is not intuitive to get a picture of this supercon-
Page 1:
VARIATIONAL STUDY OF STRONGLY CORRE
Page 4 and 5:
4 Abstract
Page 6 and 7:
6 Version abrégée
Page 8 and 9:
8 Acknowledgments check that our di
Page 10 and 11:
10 Acknowledgments
Page 12 and 13:
12 CONTENTS 3.3.5 Order parameters
Page 14 and 15:
14 CONTENTS
Page 16 and 17:
16 CHAPTER 1. INTRODUCTION c Ba 2+
Page 18 and 19:
18 CHAPTER 1. INTRODUCTION the CuO
Page 20 and 21:
20 CHAPTER 1. INTRODUCTION local Co
Page 22 and 23:
22 CHAPTER 1. INTRODUCTION that the
Page 24 and 25:
24 CHAPTER 1. INTRODUCTION (Haldane
Page 26 and 27:
26 CHAPTER 1. INTRODUCTION This can
Page 28 and 29:
28 CHAPTER 1. INTRODUCTION A(r) by
Page 30 and 31:
30 CHAPTER 1. INTRODUCTION • In C
Page 32 and 33:
32 CHAPTER 2. NUMERICAL METHODS The
Page 34 and 35:
34 CHAPTER 2. NUMERICAL METHODS Sin
Page 36 and 37:
36 CHAPTER 2. NUMERICAL METHODS pai
Page 38 and 39:
38 CHAPTER 2. NUMERICAL METHODS Whe
Page 40 and 41:
40 CHAPTER 2. NUMERICAL METHODS var
Page 42 and 43:
Page 44 and 45:
Page 46 and 47:
46 CHAPTER 2. NUMERICAL METHODS kno
Page 48 and 49:
48 CHAPTER 2. NUMERICAL METHODS wit
Page 50 and 51:
Page 52 and 53:
52 CHAPTER 3. T-J MODEL ON THE TRIA
Page 54 and 55:
Page 56 and 57:
Page 58 and 59:
Page 60 and 61:
Page 62 and 63:
Page 64 and 65:
Page 66 and 67:
Page 68 and 69:
Page 70 and 71:
Page 72 and 73:
Page 74 and 75:
Page 76 and 77:
Page 78 and 79:
Page 80 and 81:
Page 82 and 83:
Page 84 and 85:
84 CHAPTER 4. HONEYCOMB LATTICE sup
Page 86 and 87:
86 CHAPTER 4. HONEYCOMB LATTICE B A
Page 88 and 89:
88 CHAPTER 4. HONEYCOMB LATTICE •
Page 90 and 91:
90 CHAPTER 4. HONEYCOMB LATTICE mak
Page 92 and 93:
92 CHAPTER 4. HONEYCOMB LATTICE 0 e
Page 94 and 95:
94 CHAPTER 4. HONEYCOMB LATTICE /3
Page 96 and 97:
96 CHAPTER 4. HONEYCOMB LATTICE Spi
Page 98 and 99:
98 CHAPTER 4. HONEYCOMB LATTICE pos
Page 100 and 101:
100 CHAPTER 4. HONEYCOMB LATTICE -0
Page 102 and 103:
102 CHAPTER 4. HONEYCOMB LATTICE 0.
Page 104 and 105:
104 CHAPTER 4. HONEYCOMB LATTICE M=
Page 106 and 107:
106 CHAPTER 4. HONEYCOMB LATTICE 0.
Page 108 and 109:
108 CHAPTER 4. HONEYCOMB LATTICE Or
Page 110 and 111:
110 CHAPTER 4. HONEYCOMB LATTICE
Page 112 and 113: 112 CHAPTER 5. THE FLUX PHASE FOR T
Page 134 and 135: 134 CHAPTER 6. ORBITAL CURRENTS IN
Page 176 and 177: 176 CHAPTER 7. CONCLUSION is the st
Page 178 and 179: 178 CHAPTER 7. CONCLUSION although
Page 180 and 181: 180 BIBLIOGRAPHY [17] E. Dagotto. R
Page 182 and 183: 182 BIBLIOGRAPHY [59] F. F. Assad.
Page 184 and 185: 184 BIBLIOGRAPHY [98] M. Posternak,
Page 186 and 187: 186 BIBLIOGRAPHY [136] B. Fauqué,
Page 188 and 189: 188 BIBLIOGRAPHY
Page 190 and 191: 190 APPENDIX A. DETERMINANTS AND PF
Page 192 and 193: 192 APPENDIX B. A PAIR OF PARTICLES
Page 198 and 199: Education • Reviewer activity at
Page 200 and 201: 2. Model of strongly correlated ele
Page 202 and 203: List of publications 1. Ising Trans
Page 204: Schools, workshops and conferences
show all

pdf, 9 MiB - Infoscience - EPFL

Create successful ePaper yourself

Delete template?

Save as template?