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194 APPENDIX B. A PAIR OF PARTICLES IN A CUO 4 CLUSTER Nevertheless, we found in the three-band Hubbard model that the wavefunction with (α 1 ,α 2 ) lying in the long-dashed rectangular box of Fig.B.2 was optimal. This later wavefunction has a current pattern which is similar to the θ 2 phase of C.Varma, but has reversed current lines on the oxygen-oxygen bonds, and the amplitude of these lines is small. On the other hand, we measured the corresponding mean-field operator that are defined by : ĵ MF kl = ∑ σ it kl e iθ kl c † iσ c jσ + c.c. (B.11) ˆK MF kl = ∑ σ t kl e iθ kl c † iσ c jσ + c.c. (B.12) We show in Fig.B.3 the range of parameters (α 1 ,α 2 ) that are stabilized in variational Monte-Carlo calculations (short-dashed rectangular box). For the corresponding range of parameters the mean-field current operator is identical to the θ 2 phase of C. Varma, with strong currents on the oxygen-oxygen bonds. In conclusion, the variational calculations stabilize a wavefunction that has a flux through the periodic boundaries and a weak current on the oxygen-oxygen links when the physical current observable ĵ is considered, but the same wavefunction would have a true current circulation inside the triangle plaquettes when the mean-field current operator j MF is measured in this same wavefunction.
195 j Cu-O K Cu-O j O-O K O-O Figure B.2: Operator j and K measured in a wavefunction with flux parameters α 1 and α 2 (see text). The short-dashed box indicates the region where the current pattern is orientated like the θ 2 pattern by Chandra Varma. The long-dashed box indicates the region of parameters that is stabilized in the 3-band Hubbard model. α 1 and α 2 are in units of 2π.
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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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22 CHAPTER 1. INTRODUCTION that the
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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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34 CHAPTER 2. NUMERICAL METHODS Sin
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36 CHAPTER 2. NUMERICAL METHODS pai
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38 CHAPTER 2. NUMERICAL METHODS Whe
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40 CHAPTER 2. NUMERICAL METHODS var
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46 CHAPTER 2. NUMERICAL METHODS kno
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48 CHAPTER 2. NUMERICAL METHODS wit
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52 CHAPTER 3. T-J MODEL ON THE TRIA
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88 CHAPTER 4. HONEYCOMB LATTICE •
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108 CHAPTER 4. HONEYCOMB LATTICE Or
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110 CHAPTER 4. HONEYCOMB LATTICE
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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
Page 192 and 193: 192 APPENDIX B. A PAIR OF PARTICLES
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