Very soon after the discovery of the high-Tc cuprate superconductors Anderson proposed the key to understanding their highly unusual properties lay in the ansatz that they were hole doped spin liquids in which the spins are bound in singlet pairs resonating between different configurations. This RVB concept is generally formulated for a doped Mott insulator, i.e. for a system with a strong onsite Coulomb interaction. It is instructive to explore the approach from weak Coulomb interaction to see if similar behavior can also occur case. Quasi-one dimensional systems in the form of finite width ladders do indeed show such behavior with a continuous crossover from weak to strong interaction limits. In two dimensions functional renormalization group methods have recently been developed to treat weak to moderately strong interactions. These show that similar behavior can occur in the case that the Fermi energy lies near the logarithmically divergent van Hove singularity in the density of states when the band is nearly half-filled. These methods are limited to a description of the flow to strong coupling as the energy or temperature scale is lowered. The form of the strong coupling phase can be explored by numerical techniques. However a proper theory of this phase is lacking and even a consistent phenomenological description has not yet been achieved.
Very soon after the discovery of the high-Tc cuprate superconductors Anderson proposed the key to understanding their highly unusual properties lay in the ansatz that they were hole doped spin liquids in which the spins are bound in singlet pairs resonating between different configurations. This RVB concept is generally formulated for a doped Mott insulator, i.e. for a system with a strong onsite Coulomb interaction. It is instructive to explore the approach from weak Coulomb interaction to see if similar behavior can also occur case. Quasi-one dimensional systems in the form of finite width ladders do indeed show such behavior with a continuous crossover from weak to strong interaction limits. In two dimensions functional renormalization group methods have recently been developed to treat weak to moderately strong interactions. These show that similar behavior can occur in the case that the Fermi energy lies near the logarithmically divergent van Hove singularity in the density of states when the band is nearly half-filled. These methods are limited to a description of the flow to strong coupling as the energy or temperature scale is lowered. The form of the strong coupling phase can be explored by numerical techniques. However a proper theory of this phase is lacking and even a consistent phenomenological description has not yet been achieved.
Using continuity, we derive a renormalized Hamiltonian from the parent $t\text{\ensuremath{-}}J$ model to describe the properties of underdoped cuprates. The theory is constrained to agree with the behavior at half filling, which is well described by the Arovas-Auerbach valence bond state in which bosonic spinons are paired into singlets. Spinon states evolve continuously into the doped region preserving their symmetry. We assume that moving holes rapidly destroy magnetic order, which leads to a gap in the spinon spectrum and strongly renormalizes the theory. The spin gap leads to two different types hopping terms for renormalized holes. In one, a fermionic holon hops within the same sublattice accompanied by a singlet backflow, giving rise to a non-Fermi-liquid normal state with novel properties. Spinon singlets condense below a pseudogap temperature ${T}^{\ensuremath{\ast}}$ (< spin gap temperature T0), which allows holons to propagate coherently, forming a spinless Fermi liquid, but without an observable holon Fermi surface. Above ${T}^{\ensuremath{\ast}}$, holons are localized. This is the so-called strange metal phase, which is actually a new type of insulator since its resistivity would be infinite at T=0. In the second term a pair of holons belonging to opposite sublattices hop, accompanied by a singlet backflow. In the presence of the singlet condensate holon pairs condense, leading to d-wave superconductivity; the symmetry is primarily determined by the symmetry of the valence bond state at half filling. The metal and the superconductor preserve the two-sublattice character of the valence bond state. A careful examination of the nuclear magnetic resonance, tunneling, and transport data shows that the predictions of the theory is consistent with experimental results. Remarkably, the existence of the spin gap provides a natural explanation for the phenomenon of two dimensionality of the normal state in the presence of interplane hopping. The marked asymmetry between hole-doped and electron-doped cuprates is also easily explained.
Cooper pairing instability in a Fermi liquid is well understood by the BCS theory, but pairing mechanism for doped Mott insulators still remains elusive. Previously it has been shown by density matrix renormalization group (DMRG) method that a single doped hole is always self-localized due to the quantum destructive interference of the phase string signs hidden in the t-J ladders. Here we report a DMRG investigation of hole binding in the same model, where a novel pairing-glue scheme beyond the BCS realm is discovered. Specifically, we show that, in addition to spin pairing due to superexchange interaction, the strong frustration of the phase string signs on the kinetic energy gets effectively removed by pairing the charges, which results in strong binding of two holes. By contrast, if the phase string signs are "switched off" artificially, the pairing strength diminishes significantly even if the superexchange coupling remains the same. In the latter, unpaired holes behave like coherent quasiparticles with pairing drastically weakened, whose sole origin may be attributed to the resonating-valence-bond (RVB) pairing of spins. Such non-BCS pairing mechanism is therefore beyond the RVB picture and may shed important light on the high-T(c) cuprate superconductors.
We use an effective Hamiltonian for two-dimensional Hubbard model including an antiferromagnetic spin-spin coupling term to study recently proposed Gossamer superconductivity. We apply a renormalized mean field theory to approximately take into account the strong correlation effect in partially projected Gutzwiller wave functions. At the half-filling, there is a first order phase transition to separate a Mott insulator at large Coulomb repulsion U from a Gossamer superconductor at small U. At the critical value U=Uc, the charge carrier density and the superconducting (SC) order parameter change discontinuously from zero in the Mott insulating phase to finite values in the Gossamer SC phase. The first order transition is due to the interplay of the kinetic and spin exchange energies. As the electron density changes away from half-filling, the Gossamer SC state changes smoothly, while the Mott insulator is evolved into a resonating valence bond (RVB) SC state. The Gossamer and RVB SC states have the same pairing symmetry. The SC order parameter changes smoothly from a RVB SC state at U>Uc to a Gossamer SC state at U<Uc at a fixed nonhalf-filled electron density. We argue that the RVB SC state is smoothly connected to the Gossamer SC state, hence to the BCS state.
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.
The discovery of high-Tc superconductivity in the cuprates, and the observation that strong correlations are important in connection with these compounds has led to a tremendous interest in understanding the physics of strongly correlated electronic models. In particular the two simplest models for strongly correlated electrons, namely the Hubbard and t–J models, have been the subject of intensive studies. In a milestone paper of 1987, P.W. Anderson proposed that a resonating valence bond (RVB) wave-function, which consists of a superposition of valence-bond states, contains the ingredients to account for a consistent theory of the Hubbard and t–J models. Motivated by the success of variational Monte- Carlo to describe some of the peculiar properties of the cuprates, we propose in this dissertation, on one hand, to extend the method to further strongly correlated models to describe other compounds such as graphene, carbon nanotube or the cobaltite compounds, and on the other hand we propose to focus on the pseudo-gap phase of the cuprates, which is still prompting for a consistent theory. In particular, the issue of checkerboard spatial modulations in the density of states in the low temperature regime of the cuprates is addressed. Finally, we have studied the possibility for spontaneous orbital currents in the cuprates, that might play a key role in the theory of high Tc superconductors.
In a recent review by Anderson and co-workers, it was pointed out that an early resonating valence bond (RVB) theory is able to explain a number of unusual properties of high-temperature superconducting (SC) Cu oxides. Here we extend previous calculations to study more systematically the low-energy physical properties of the plain vanilla d-wave RVB state, and to compare the results with the available experiments. We use a renormalized mean-field theory combined with variational Monte Carlo and power Lanczos methods to study the RVB state of an extended $t\text{\ensuremath{-}}J$ model in a square lattice with parameters suitable for the hole-doped Cu oxides. The physical observable quantities we study include the specific heat, the linear residual thermal conductivity, the in-plane magnetic penetration depth, the quasiparticle energy at the antinode $(\ensuremath{\pi},0)$, the superconducting energy gap, the quasiparticle spectra, and the Drude weights. The traits of nodes (including kF, the Fermi velocity vF, and the velocity along Fermi surface v2), and the SC order parameter are studied. Comparisons of the theory and the experiments in cuprates show an overall qualitative agreement, especially on their doping dependences.