Resonating Valence Bond State Research Articles

Dimer–resonating valence bond state of the four-leg Heisenberg ladder: Interference among resonances

We study the ground state of the four-leg spin ladder using a dimer--resonating valence bond (RVB) ansatz and the Lanczos method. Besides the well-known resonance mechanism between valence bond configurations we find interference effects among nearby resonances. These effects were missed by standard factorizing approaches to the RVB states.

Recurrent variational approach to the two-leg Hubbard ladder

We applied the Recurrent Variational Approach to the two-leg Hubbard ladder. At half-filling, our variational Ansatz was a generalization of the resonating valence bond state. At finite doping, hole pairs were allowed to move in the resonating valence bond background. The results obtained by the Recurrent Variational Approach were compared with results from Density Matrix Renormalization Group.

Spin-charge separation in strongly correlated electronic systems

The spin-charge separation (SCS) in 1D and 2D are discussed from the viewpoint of gauge theory. For 1D I discuss the angle-resolved photoemission spectra (ARPES), which show clear evidence for the spin-charge separation. For 2D the underdoped cuprates are discussed, where the three classes of electronic state, i.e., the Néel state (N), the valence-bond solid (VBS) state and the resonating-valence-bond (RVB) state, are relevant. These states can be understood in terms of the competition between (i) magnetic ordering versus singlet formation and (ii) confinement versus deconfinement of the gauge field. It is fairly easy to understand the former, (i), but the latter, (ii), is more subtle and has not yet been established. I argue that the deconfining phase, i.e., the RVB state, is a new state of matter with SCS, and is realized when the sheet resistance is less than a critical value of the order of the quantum resistance . This condition is equivalent to that for superconductivity in the Josephson network model. The anomalous Kondo effect due to the non-magnetic impurities doped into the system reflects the non-Fermi-liquid nature of the host electronic state, and hence is the most promising experimental evidence for this new state of matter. We put special emphasis on the residual resistivity, and propose that its value provides a clear test for SCS.

Orbital Frustration and Resonating Valence Bond State in the Spin-1/2 Triangular Lattice LiNiO 2

From the 7 Li nuclear magnetic resonance (NMR) and specific heat measurements of LiNiO 2 , consisting of a spin-1/2 triangular lattice, it is demonstrated that the previously suggested spin-glass-like freezing below T s g =8 K, which is caused by defects of Li ions, is not the true ground state, but rather a quantum disordered state is realized without a spin gap. This state is characterized by power-law behavior of the temperature dependence of the specific heat below 0.5 K. A spin-liquid state with short-range ferromagnetic correlations is suggested from new insight into the frustration of orbital ordering for doubly degenerate e g shells in the triangular lattice.

The d-wave resonance valence bond state

The properties of strongly correlated electron models in the form of ladders are reviewed. The groundstate of undoped and lightly doped two chain ladders described by the t-J model is a realization of a d-wave resonance valence bond state. Although many properties are those of lightly doped insulators, the strong magnetic polarizability modifies the dispersion relation for quasiparticles to resemble a metal with a large Fermi surface. Some discussion is given of possible relationships of the ladder systems to a two dimensional planar t-J model and of a possible origin of the spin-gap in underdoped cuprates.

Exact eigenvalues and thermodynamics of the 4 × 4 triangular Heisenberg antiferromagnet

The full energy spectrum and all the eigenstates of the antiferromagnetic Heisenberg hamiltonian of the 4 × 4 triangular lattice with periodic boundary conditions and s= 1 2 are obtained by means of an exact diagonalization of the Hamiltonian. To this end we employ the method of hierarchy of algebras of spin systems. The specific heat, the entropy and the susceptibility of the system are discussed and compared with those of the 4 × 4 square lattice. Our results strongly support the original conjecture made by Anderson that the ground state of the triangular Heisenberg antiferromagnet is the resonating valence bond state.

The resonating valence bond state and high-T c superconductivity — a mean field theory

A mean field type theory is developed for the insulating RVB state and high temperature superconductivity in doped La 2 CuO 4 and other high- T c oxides. The T c as a function of the doping parameter δ drops sharply around ▪ ∼ δ. The zero temperature gap versus T c relation depends sensitively on the choice of the parameters. Gutzwiller projection, suppression of T c by phase fluctuations for small δ and screening effects are briefly discussed.

Loop coverings of two dimensional square lattices

In a two dimensional square lattice, where all sites are covered by loops, in the past few years a classical statistical mechanics model of dense loop gas was considered for its relevance for the evaluation of observables of the quantum antiferromagnetic Heisenberg model on the resonating valence bond state. By use of transfer matrices we evaluate several observables for narrow strips with a width of two or three sites. A simple extrapolation, consistent with rigorous bounds, is conjectured for its possible use in a variational ansatz in the Hubbard model.

TiOCl, TiOBr-are these RVB d1, S=1/2 materials? The results of scandium substitution set in the context of other S=1/2 systems of current interest for high-temperature superconductivity and the metal-insulator transition

The title materials display anomalous electrical, magnetic and optical properties. They have the characteristics of Mott insulators showing high electrical resistance and ligand-field optical spectra, but at the same time they adopt a magnetic ground state which is neither of Curie-Weiss type nor indeed of some standard antiferromagnetically ordered condition. The observed state is one of lowish, isotropic, and almost temperature-independent paramagnetism. The authors have studied the magnetic properties of Sc-doped TiOX, seeking possible indications of the existence of the resonant valence bond or RVB state-the state currently suggested by some to be responsible for high-temperature superconductivity in the mixed-valence cuprates. It is necessary to distinguish between RVB and some extreme case of magnetic frustration in these S=1/2, 2D oxyhalide systems. The authors' tentative conclusion is that TiOX presents an RVB ground state which Sc doping renders glassy and static.

Pairing of two-dimensional fermions due to singular interactions.

We study a finite-temperature spectrum renormalization and s-wave pairing instability in a system of fermions with an attractive ``current-current'' interaction mediated by an overdamped mode with a dispersion \ensuremath{\omega}=i${\mathrm{\ensuremath{\Gamma}}}^{\mathrm{\ensuremath{-}}1}$${\mathit{q}}^{2+\mathrm{\ensuremath{\eta}}}$, 0\ensuremath{\le}\ensuremath{\eta}\ensuremath{\le}1. It generalizes the case of a transverse gauge interaction between spinons in Mott insulators, which drives an instability of a homogeneous resonant valence bond state towards a dimerization.

Phonon-Raman scattering in a correlated superconductor

The phonon spectral density function is calculated to explain the observed anomalies in the Raman spectrum of the cuprate superconductors. These being strongly correlated systems, their ground state is taken to be the resonating valence bond (RVB) state. In this state, the phonons are shown to couple predominantly to the RVB pair excitations besides the usual interaction with the charge carrier density. It is proposed that the superconductivity in the system appears due to the correlation bag mechanism where the collective excitations of the RVB state mediate an attractive interaction between the charge carriers which leads to pairing. The dependence of the transition temperature on the RVB gap parameter as well as the dopant concentration is demonstrated. The phonon self-energies, which involve the pair correlation function and the density response function, are evaluated at zero temperature for the normal state as well as the superconducting states. It is shown that the pair correlation function strongly renormalises the phonon spectrum. Its spectral density shows a broad peak corresponding to the RVB-amplitude mode, which qualitatively resembles the observed Raman spectrum in the superconducting state.

Effect of the intersite Coulomb interaction in the extended Hubbard model.

Starting from the large-U Hubbard model combining the intersite Coulomb interaction V, we investigate the competition, on a square lattice, between the d-wave resonating-valence-bond (RVB) state and the staggered-flux-phases (SFP) state on the basis of F. C. Zhang's earlier work [Phys. Rev. Lett. 64, 974 (1990)]. We find that a very small V (0.1U) may help stabilize the SFP state by effectively suppressing the d-wave pairing amplitude and enhance the particle-hole correlation. We show in the phase diagram of V-\ensuremath{\delta} (the doping concentration) the critical curve of ${\mathit{V}}_{\mathit{c}}$(\ensuremath{\delta}) below which the RVB state is energetically favored while beyond this point a mixed state of SFP and RVB occurs, which has the lowest energy. We also find that the pure SFP state is not the most stable state in the whole V region.

Erratum: Motion of a single hole in a resonating-valence-bond background: Some exact results

An antiferromagnetic spin model ({ital S}=1/2) consisting of a chain of octahedra is considered. In a certain parameter regime of the Hamiltonian the exact ground state is a local resonating-valence-bond (RVB) state. We start with the {ital t}-{ital J} Hamiltonian for this model describing a single hole in the system and derive exact ground and excited states of the Hamiltonian when the hole is static. The local spin distortion around a hole is termed a spin polaron. The dynamics of the hole is studied through construction of exact eigenstates describing spin polarons in extended states. Coherent states for all momentum wave vectors in the chain direction exist for certain spin polarons. In the Nagaoka limit, the RVB polaronic states have energy greater than that of the ferromagnetic state. For exchange interaction {ital J}{ne}0, the RVB states have lower energy. Other exact states obtained include states in which the hole motion is localized. Structural similarity of the present model to the arrangement of Cu spins in La{sub 2}CuO{sub 4} is also highlighted.

Fermi Surface and Spin Fluctuations in Extendedt-JModel

The spin fluctuations in the extended t - J model have been investigated in the slave-boson mean-field theory by extending the early work by Suzumura et al. [J. Phys. Soc. Jpn. 57 (1988) 2768] based on both uniform and singlet RVB (Resonating Valence Bond). By choosing the transfer integrals to reproduce the Fermi surface of LSCO and YBCO, which is essentially rotated by 45°, it is found that incommensurate spin fluctuations can be expected for the Fermi surface of LSCO type, whereas only commensurate ones for that of YBCO type, in agreement with experiments. Moreover, the Knight shift is shown to decrease as the temperature is lowered in the presence of the singlet RVB, while it is essentially independent of temperature in the uniform RVB state. These two cases correspond to, in our classification, T c =60 K and T c =90 K YBCO systems, which also agrees with the qualitative difference observed experimentally.

Staggered flux phase and d-wave phase of the t-J model

The authors have numerically evaluated the energy of the staggered flux phase state (SFP), the d-wave resonating valence bond state, and the mixed SFP and d-wave state (SFP+d) of the extended t-J model at various hole densities ( delta ). The flux per plaquette and the size of the d-wave gap are taken as variational parameters. The calculation includes the kinetic energy, spin energy, the effective hole-hole interaction and the three-site pair-hopping term. They found that the SFP is stable against the projected Fermi liquid up to delta approximately=20%. For moderately large J, J/t>or=0.4, the SFP+d state may be favoured against the pure d-wave state but only at very low hole density ( delta approximately 20%). These calculations show that the pure SFP state is never the ground state at hole densities of experimental interest.

Analytic evaluation of resonating valence bond states

Expectation values of the one-particle density matrix, the Cooper-pair amplitude and the Hubbard interaction are calculated analytically within locally correlated superconducting wave functions. For weak correlations or small densities, a rapidly converging series-expansion of exact expectation values is derived, while for strong correlations a sum-rule conserving single-site approximation is developed. Explicit results for the kinetic energy of holes within resonating valence bond states are compared with corresponding Monte Carlo data. The characteristic difference between wave functions with fixed and variable particle number, respectively, is pointed out.

Motion of a single hole in a resonating-valence-bond background: Some exact results.

An antiferromagnetic spin model (S=1/2) consisting of a chain of octahedra is considered. In a certain parameter regime of the Hamiltonian the exact ground state is a local resonating-valence-bond (RVB) state. We start with the t-J Hamiltonian for this model describing a single hole in the system and derive exact ground and excited states of the Hamiltonian when the hole is static. The local spin distortion around a hole is termed a spin polaron. The dynamics of the hole is studied through construction of exact eigenstates describing spin polarons in extended states. Coherent states for all momentum wave vectors in the chain direction exist for certain spin polarons. In the Nagaoka limit, the RVB polaronic states have energy greater than that of the ferromagnetic state. For exchange interaction J\ensuremath{\ne}0, the RVB states have lower energy. Other exact states obtained include states in which the hole motion is localized. Structural similarity of the present model to the arrangement of Cu spins in ${\mathrm{La}}_{2}$${\mathrm{CuO}}_{4}$ is also highlighted.

Spontaneously dimerized ground states in 1D frustrated Heisenberg antiferromagnets

We give an explicit proof that the completely dimerized (’Kekulè or nearest-neighbor resonant valence bond) state is the degenerate ground state of a linear chain S =1/2 Heisenberg antiferromagnet, with competing couplings extending up to 2n nearest neighbors, if the relation J1 = 2n, J2 = 2n − 1,...,J2n = 1, holds between the various exchange integrals. The previously known result for J2 =1/2 J1 is then just a special case corresponding to n=1. We study in detail n=2 (fourth-nearest neighbors) and show that this state is the ground state of the Hamiltonian when J1 − 2J2 + J3 = 0, J3 = 2J4, in a finite interval of values of the parameter J4. A rigorous lower limit for the extension of this interval is found to be 0 ≤ J4 ≤1/4 J1. A comparison with ground-state configurations of the equivalent classical Heisenberg and Ising models is made.

Slave-boson method for the Hubbard model: Resonating-valencebond state and high-temperature superconductivity

The modified “slave-boson” method is used to describe the metal-insulator and metal-superconductor phase transitions in the Hubbard model. Expressions are derived for the energy gap and phase-transition temperature.

Competition and possible coexistence of flux and resonating-valence-bond phases in the t-J model.

The competition and possible coexistence of the flux phase and pairing states are considered within the slave-boson approach. In addition to the gauge field, coupling holons, and spinons, a statistical gauge field is introduced to account for the hard-core nature of holons. Using the equivalence of \ensuremath{\pi}-uniform and -staggered fluxes, we show the possibility of reducing the staggered flux and guaranteeing the commensurability condition of the uniform flux for holons at the same time. For certain dopings the frustration of the spinon gauge field to holon motion can be compensated by the holon's own statistical gauge field. Contrary to earlier conclusions of other authors, we find that the flux phase can coexist with the resonating-valence-bond (RVB) states below a critical doping concentration ${\mathrm{\ensuremath{\delta}}}_{\mathit{c}}$, beyond which the d-wave RVB state takes over.