This paper compares the kinetic energy of holes in the antiferromagnetic (AF) state and in an approximate singlet liquid wave function of the Resonating Valence Bond type (RVB), with only nearest neighbour singlet pairing. The atomic interaction U of the Hubbard model is taken to be large compared with the band width 8 t . In the limit 8 t / U →0, I find that the hole kinetic energy is at most as low in RVB than in AF, but there are indications that it is in fact lower in AF. At finite t / U , the comparison between AF and RVB depends on corrections of order t / U which are not known yet for RVB, but which should be of the same order as in AF. As a restult within the simplest Hubbard model with nearest neighbour hopping, it is unlikely that a small concentration of holes can stabilize RVB if the latter is less stable than AH at half band filling.
This paper compares the kinetic energy of holes in the antiferromagnetic (AF) state and in an approximate singlet liquid wave function of the Resonating Valence Bond type (RVB), with only nearest neighbour singlet pairing. The atomic interaction U of the Hubbard model is taken to be large compared with the band width 8 t . In the limit 8 t / U →0, I find that the hole kinetic energy is at most as low in RVB than in AF, but there are indications that it is in fact lower in AF. At finite t / U , the comparison between AF and RVB depends on corrections of order t / U which are not known yet for RVB, but which should be of the same order as in AF. As a restult within the simplest Hubbard model with nearest neighbour hopping, it is unlikely that a small concentration of holes can stabilize RVB if the latter is less stable than AH at half band filling.
We have calculated the energy of the resonating-valence-bond (RVB) state made of nearest-neighbor singlet pairs in the two-dimensional Hubbard model at half filling and the energy of holes in the RVB state near half filling. The energy of the RVB state was obtained by extrapolating the result in a 6\ifmmode\times\else\texttimes\fi{}6 square lattice with the periodic boundary condition to the infinite lattice. The energy of holes was obtained by examining the first five moments of the density of states of holes in the RVB state. We find that the holes are more stabilized in the RVB state than in the N\'eel state for J/t\ensuremath{\gtrsim}0.1, where J and t are the exchange interaction and the nearest-neighbor hopping integral, respectively. We discuss the possibility of the RVB state in the high-Tc Cu oxides.
The effective Hamiltonian of strongly correlated electrons on a square lattice is replaced by a renormalised Hamiltonian and the factors that renormalise the kinetic energy of holes and the Heisenberg spin-spin coupling are calculated using a Gutzwiller approximation scheme. The accuracy of this renormalisation procedure is tested numerically and found to be qualitatively excellent. Within the scheme a resonant valence bond (RVB) wavefunction is found at half-filling to be lower in energy than the antiferromagnetic state. If the wavefunction is expressed in fermion operators, local SU(2) and U(1) invariance leads to a redundancy in the representation. The introduction of holes removes these local invariances and the authors find that a d-wave RVB state is lowest in energy. This state has a superconducting order parameter whose amplitude is linear in the density of holes.
The effective Hamiltonian of strongly correlated electrons on a square lattice is replaced by a renormalised Hamiltonian and the factors that renormalise the kinetic energy of holes and the Heisenberg spin-spin coupling are calculated using a Gutzwiller approximation scheme. The accuracy of this renormalisation procedure is tested numerically and found to be qualitatively excellent. Within the scheme a resonant valence bond (RVB) wavefunction is found at half-filling to be lower in energy than the antiferromagnetic state. If the wavefunction is expressed in fermion operators, local SU(2) and U(l) invariance leads to a redundancy in the representation. The introduction of holes removes these local invariances and we find that a d-wave RVB state is lowest in energy. This state has a superconducting order parameter whose amplitude is linear in the density of holes.
We describe a new method to numerically evaluate the properties of correlated superconducting wave functions. We have applied it to the resonating-valence-bond (RVB) wave function for the Hubbard model on the square lattice. For the half-filled case we find that the d-wave RVB state and the antiferromagnetic ordered state have the same energy within numerical accuracy. At 10% doping we find d-wave superconductivity, consistent with previous studies. We show that the superconducting order parameter is proportional to the number of holes, for small hole concentrations.
The Hubbard model in D dimensions, with the on-site repulsion U and the transfer integral between nearest neighbors −t/D, is studied on the basis of the Kondo-lattice theory. If U/∣t∣≫1, ∣n−1∣≲∣t∣/(DU), where n is the number of electrons per unit cell, and D is so small that ∣J∣/D≫kBTc, where J=−4t2/U and Tc is 0K for D=1 and is the highest critical temperature among possible ones for D≥2, a low-T phase where Tc<T≪∣J∣/(kBD) is a frustrated electron liquid. Since the liquid is stabilized by the Kondo effect in conjunction with the resonating-valence-bond (RVB) mechanism, it is simply the RVB electron liquid; in one dimension, it is also the Tomonaga-Luttinger liquid. The Kondo energy of the RVB liquid is kBTK=O(∣J∣/D); its effective Fermi energy is O(kBTK). A midband appears on the chemical potential between the upper and lower Hubbard bands; the Hubbard gap is a pseudogap. As regards the density of states per unit cell of the midband, its bandwidth is O(kBTK) or O(∣J∣/D), its peak height is O(1/U), and its spectral weight is O[t2/(DU2)]. Since the midband almost disappears in the Heisenberg limit, the RVB electron liquid in the Heisenberg limit is simply the RVB spin liquid. The RVB electron and spin liquids adiabatically continue to each other. Since local moments form in a high-T phase where T≳TK, the high-T phase is simply the Mott insulator.