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156 CHAPTER 6. ORBITAL CURRENTS IN THE CUPRATES
w.f. Etot Tdp Tpp Ud Up ∆p Vdp variance
Lanczos −1.13821 −3.10036 −0.79666 0.26737 0.08398 1.77545 0.63201 0
Gutzwiller −0.8987(1) −3.04326 −0.88752 0.27849 0.11712 1.88523 0.75122 0.190
JA/FLUX −1.0505(1) −3.03928 −0.82504 0.27835 0.07725 1.82681 0.63139 0.051
1LS/JA/FLUX −1.0877(1) −3.06206 −0.84549 0.25164 0.08835 1.84430 0.63553 0.018
JA/RVB −1.0775(1) −3.06068 −0.83073 0.26176 0.08197 1.83466 0.64076 0.018
AFQMC/FLUX −1.0814(1) −2.73965 −0.59317 0.39413 0.04142 1.20917 0.60668 0.001
1LS/JA/RVB −1.1153(1) −3.14070 −0.83715 0.26559 0.08736 1.86495 0.64469 0.018
GFMC/JA −1.1112(5) 0.26966 0.08708 1.77314 0.63177 0.001
Table 6.1: Variational energies of the different variational wavefunctions compared with the exact diagonalization calculations
(Lanczos) done on a 8 copper lattice with 10 holes and S z = 0. We show the total energy (Etot), the kinetic energy
of the copper-oxygen links (Tdp) and of the oxygen-oxygen links (Tpp), the on-site repulsion energy of the d (Ud) andp
(Up) orbitals, the expectation value of the charge gap operator (∆p), and the expectation value of the Coulomb repulsion
between the d and p orbitals (Vdp). The Lanczos step applied on the RVB wavefunction is the best variational Ansatz
(1LS/JA/RVB) The auxiliary field Quantum Monte Carlo applied on the orbital current wavefunction (AFQMC/FLUX)
and the fixe node approximation applied on a simple Jastrow wavefunction (GFMC/JA) are also shown.
w.f. Etot variance M = √ 〈S i z Sz i+r 〉
JA/SDW −1.5742(5) 0.00148(5) 0.3200(5)
1LS/JA/SDW −1.5756(5) 0.00125(5) 0.3366(5)
GFMC/JA/SDW −1.575(2) 0.0010(5) 0.3441(5)
Table 6.2: Projected antiferromagnetic order parameter M = limr→∞√
〈S
z
i S i+r z 〉 at half-filling on a 6 × 6 copper lattice
(108 sites) for the magnetic variational wavefunction JA/SDW, for the same wavefunction improved by one lanczos step
1LS/JA/SDW, and for the fixe node method using the JA/SDW as a guiding wavefunction.