Valence Bond Correlations Research Articles

Possible coexistence of short-range resonating valence bond and long-range stripe correlations in the spatially anisotropic triangular-lattice quantum magnet Cu2 (OH) 3NO3

We show that short-range resonating valence bond correlations and long-range order can coexist in the ground state (GS) of a frustrated spin system. Our study comprises a comprehensive investigation of the quantum magnetism on the structurally disorder-free single crystal of ${\mathrm{Cu}}_{2}{(\mathrm{OH})}_{3}{\mathrm{NO}}_{3}$, which realizes the $s$ = 1/2 Heisenberg model on a spatially anisotropic triangular lattice. Competing exchange interactions determined by fitting the magnetization measured up to 55 T give rise to an exotic GS wave function with the coexistence of the dominant short-range resonating valence bond correlations and weak long-range stripe order (ordered moment ${M}_{0}=|\ensuremath{\langle}{s}_{i}^{z}\ensuremath{\rangle}|\ensuremath{\sim}0.02$). At low temperatures, a first-order spin-flop transition is visible at $\ensuremath{\sim}$1--3 T. As the applied field further increases, another two magnetic field induced quantum phase transitions are observed at $\ensuremath{\sim}$14--19 and $\ensuremath{\sim}$46--52 T, respectively. Simulations of the Heisenberg exchange model show semiquantitative agreement with the magnetic-field modulation of these unconventional phases, as well as the absence of visible magnetic reflections in neutron diffraction, thus supporting the GS of the spin system of ${\mathrm{Cu}}_{2}{(\mathrm{OH})}_{3}{\mathrm{NO}}_{3}$ may be approximate to a quantum spin liquid. Our study establishes structurally disorder-free magnetic materials with spatially anisotropic exchange interactions as a possible arena for spin liquids.

A valence bond perspective of the reaction force formalism

The reaction force formalism represents a convenient approach to analyze the course of a reaction step. From this analysis, the reaction path can be separated in a number of regions that are associated to either structural changes or electronic reorganization. This empirical observation is rationalized in this work on the basis of a simple two-state valence bond correlation diagram. We demonstrate that the ratio between the integrated reaction force and the region of interest ($$w_{\text{ii}}/w_{\text{i}}$$ for the forward reaction and $$w_{\text{iii}}/w_{\text{iv}}$$ for the backward reaction) increases with the ratio between the quantum mechanical resonance energy and the energy required to reach the crossing point at the transition state, we call to this ratio the strength of the resonance. This observation means that the size of the transition region (region ii and iii), that includes the transition state, depends on the strength of the resonance, and the structural zones (region i and iv), that are regions associated with the pure valence bond state curves (no resonance). We propose a simple analytical relationship for $$w_{\text{ii}}/w_{\text{i}}$$ and $$w_{\text{iii}}/w_{\text{iv}}$$ based on three parameters: (i) the quantum mechanical resonance energy, (ii) the energy of the reaction and (iii) the overlap between the VB structures at the transition state. The previous conclusions were supported by a reaction force analysis of a $${\text{S}}_{N}2$$ reactions, $${\text{X}}^{-} + {\text{CH}}_{3}{-}{\text{Y}} \rightarrow {{\text{X}}{-}{\text{CH}}}_{3} + {\text{Y}}^{-} ({\text{X}} = {\text{F}}, {\text{Cl}}, {\text{Br}})$$. The valence bond parameters for these reactions are estimated from empirical considerations. A very good agreement is found between the computed reaction force ratios and the predicted one.

Spin liquids in graphene

We reveal that local interactions in graphene allow novel spin liquids between the semi-metal and antiferromagnetic Mott insulating phases, identified with algebraic spin liquid and Z$_{2}$ spin liquid, respectively. We argue that the algebraic spin liquid can be regarded as the two dimensional realization of one dimensional spin dynamics, where antiferromagnetic correlations show exactly the same power-law dependence as valence bond correlations. Nature of the Z$_{2}$ spin liquid turns out to be $d + i d'$ singlet pairing, but time reversal symmetry is preserved, taking $d + i d'$ in one valley and $d - i d'$ in the other valley. We propose the quantized thermal valley Hall effect as an essential feature of this gapped spin liquid state. Quantum phase transitions among the semi-metal, algebraic spin liquid, and Z$_{2}$ spin liquid are shown to be continuous while the transition from the Z$_{2}$ spin liquid to the antiferromagnetic Mott insulator turns out to be the first order. We emphasize that both algebraic spin liquid and $d \pm id'$ Z$_{2}$ spin liquid can be verified by the quantum Monte Carlo simulation, showing the enhanced symmetry in the algebraic spin liquid and the quantized thermal valley Hall effect in the Z$_{2}$ spin liquid.

Spin-orbital resonating valence bond liquid on a triangular lattice: Evidence from finite-cluster diagonalization

We investigate the ground state of the $d^1$ spin-orbital model for triply degenerate $t_{2g}$ orbitals on a triangular lattice which unifies intrinsic frustration of spin and orbital interactions with geometrical frustration. Using full or Lanczos exact diagonalization of finite clusters we establish that the ground state of the spin-orbital model which interpolates between the superexchange and direct exchange interactions on the bonds is characterized by valence-bond correlations. In the absence of Hund's exchange the model describes a competition between various possible valence-bond states. By considering the clusters with open boundary conditions we demonstrate that orbital interactions are always frustrated, but this frustration is removed by pronounced spin singlet correlations which coexist with supporting them dimer orbital correlations. Such local configurations contribute to the disordered ground states found for the clusters with periodic boundary conditions which interpolate between a highly resonating, dimer-based, entangled spin-orbital liquid phase, and a valence-bond state with completely static spin-singlet states. We argue that these states are also realized for the infinite lattice and anticipate that pronounced transitions between different regimes found for particular geometries will turn out to smooth crossovers in the properties of the spin-orbital liquid in the thermodynamic limit. Finally, we provide evidence that the resonating spin-orbital liquid phase involves entangled states on the bonds. In such a phase classical considerations based on the mean-field theory cannot be used, spin exchange interactions do not determine spin bond correlations, and quantum fluctuations play a crucial role in the ground states and magnetic transitions.

Contractor-renormalization study of Hubbard plaquette clusters

We implement the contractor-renormalization method to study the checkerboard Hubbard model on various finite-size clusters as function of the inter-plaquette hopping t' and the on-site repulsion U at low hole doping. We find that the pair-binding energy and the spin gap exhibit a pronounced maximum at intermediate values of t' and U, thus indicating that moderate inhomogeneity of the type considered here substantially enhances the formation of hole pairs. The rise of the pair-binding energy for t'<t'_max is kinetic-energy driven and reflects the strong resonating valence bond correlations in the ground state that facilitate the motion of bound pairs as compared to single holes. Conversely, as t' is increased beyond t'_max antiferromagnetic magnons proliferate and reduce the potential energy of unpaired holes and with it the pairing strength. For the periodic clusters that we study the estimated phase ordering temperature at t'=t'_max is a factor of 2-7 smaller than the pairing temperature.

Quantum Phases in a Doped Mott Insulator on the Shastry-Sutherland Lattice

We propose the projected BCS wave function as the ground state for the doped Mott insulator SrCu2(BO3)2 on the Shastry-Sutherland lattice. At half filling this wave function yields the exact ground state. Adding mobile charge carriers, we find a strong asymmetry between electron and hole doping. Upon electron doping an unusual metal with strong valence bond correlations forms. Hole doped systems are d-wave resonating valence bond superconductors in which superconductivity is strongly enhanced by the emergence of spatially varying plaquette bond order.

D-symmetry superconductivity due to valence bond correlations

It is shown that d-symmetry superconductivity due to valence bond correlations is possible. Valence bond correlations are compatible with antiferromagnetic spin order. In order to explictly construct a homogeneous state with the valence bond structure in the two-dimensional Hubbard model for an arbitrary doping, we have used the variational method based on unitary local transformation. Attraction between holes in the d-channel is due to modulation of hopping by the site population in course of the valence bond formation, and corresponding parameters have been calculated variationally. An important factor for the gap width is the increase in the density of states on the Fermi level due to antiferromagnetic splitting of the band. The gap width and its ratio to the Tc are 2Δ≃0.1t and 2Δ/kTc≃4.5−4 for U/t≃8. The correspondence between the theoretical phase diagram and experimental data is discussed. The dependence of Tc on the doping δ=|n−1| and the Fermi surface shape are highly sensitive to the weak interaction t′ leading to diagonal hoppings. In the case of t′>0 and p-doping, the peak on the curve of Tc(δ) occurs at the doping δopt, when the energy of the flattest part of the lower Hubbard subband crosses the Fermi level at k∼(π,0). In underdoped samples with δ<δopt, the anisotropic pseudogap in the normal state corresponds to the energy difference |E(π,0)−μ| between this part of the spectrum and the Fermi level.

D-Symmetry superconductivity as a consequence of valence-bond type correlations

It is shown that dx2−y2 symmetry of superconducting order due to valence bond (VB) type correlations is possible. The VB correlations are compatible with antiferromagnetic (AF) spin order. For the two-dimensional Hubbard model with arbitrary doping, the variational method of local unitary transformations is used to construct explicitly a uniform state with VB structure. The d-channel attraction of holes is a consequence of the modulation of hops by the populations of centers accompanying VB formation, and the parameters of the modulation are determined variationally. The increase in the density of states at the Fermi level accompanying AF splitting of the band, which is absent in the paramagnetic state, is important for the gap width. The gap width and its ratio to Tc are of the order of 2Δ≃0.1t and 2Δ/kTc≃4–4.5 with U/t≃8. The agreement between the phase diagram found and experiment is discussed.

Valence bond mapping of antiferromagnetic spin chains

Boson mapping techniques are developed to describe valence bond correlations in quantum spin chains. Applying the method to the alternating bond hamiltonian for a generic spin chain, we derive an analytic expression for the transition points which gives perfect agreement with existing Density Matrix Renormalization Group (DMRG) and Quantum Monte Carlo (QMC) calculations.

Physical manifestations of valence-bond structures in correlated systems

Using the Hubbard model and the corresponding t-J model, we study the properties of correlated states with valence-bond structures. Mixed states with such structures and with antiferromagnetic spin ordering can be constructed by means of local unitary transformations of uncorrelated states. The latter turn out to have lower energy than mean-field antiferromagnetic solutions. Spin correlations for various degrees of doping δ=n−1 are in good agreement with the results of exact calculations for finite systems. In contrast to mean-field solutions, allowance for valence-bond correlations leads to a reasonable value of the critical δ, at which long-range antiferromagnetic order disappears. A calculation of the spectral functions that describe photoemission reveals typical behavior in two bands of effective hole (and electron) excitations, and energy transport in bands as the quasimomentum varies from (0,0) to (π,π), consistent with calculations in finite systems. We construct a homogeneous correlated state of fluctuating valence bonds (the band-model analog of states of fluctuating valence bonds), and demonstrate that its energy is lower than that of valence-bond alternant structures.

Qualitative valence bond analysis of (10-S-4) sulfuranes and (9-S-3) sulfuranyl radicals

Valence-bond (VB) correlation diagrams are used for the analysis of sulfur hypervalent compounds. It is shown that the stability of (10-S-4) sulfuranes is closely related to the electronegativity of the apical substituents. Moreover, it is predicted that an antisymmetrical bond stretch of apical bonds is easier with less-electronegative substituents. The electronic structure of (9-S-3) sulfuranyl radicals is analyzed by means of ab initio calculations. VB correlation diagrams are then used to discuss the factors which favor the σ or π nature of these radicals. Qualitative arguments are developed for predicting the possible metastability of these radicals.

A nearly diabatic description of S N2 reactions: The collinear H 3− model

A simple “diabatization” procedure of MO CI calculations, supporting Shaik's valence bond correlation diagrams, is proposed for the H 3 − system. It is shown that, in this S N2 reaction, two nearly diabatic surfaces correlating the ground state of the reactant to the first charge-transfer excited state of the products (and vice versa) can generate the two lowest adiabatic surfaces.

Valence bond analysis of hypervalent sulphur compounds

Some characteristic structural features of hypervalent R2SL2 species are interpreted by means of valence bond correlation diagrams.