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Register a new userResonating Valence Bond States with Trimer Motifs
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The trimer resonating valence bond (tRVB) state consisting of an equal-weight superposition of trimer coverings on a square lattice is proposed. A model Hamiltonian of the Rokhsar-Kivelson type for which the tRVB becomes the exact ground state is written. The state is shown to have $9^g$ topological degeneracy on genus g surface and support $Z_3$ vortex excitations. Correlation functions show exponential behavior with a very short correlation length consistent with the gapped spectrum. The classical problem of the degeneracy of trimer configurations is investigated by the transfer matrix method.
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An isotropic anti-ferromagnetic quantum state on a square lattice is characterized by symmetry arguments only. By construction, this quantum state is the result of an underlying valence bond structure without breaking any symmetry in the lattice or spin spaces. A detailed analysis of the correlations of the quantum state is given (using a mapping to a 2D classical statistical model and methods in field theory like mapping to the non-linear sigma model or bosonization techniques) as well as the results of numerical treatments (regarding exact diagonalization and variational methods). Finally, the physical relevance of the model is motivated. A comparison of the model to known anti-ferromagnetic Mott-Hubbard insulators is given by means of the two-point equal-time correlation function obtained i) numerically from the suggested state and ii) experimentally from neutron scattering on cuprates in the anti-ferromagnetic insulator phase.
We apply a variational wave function capable of describing qualitatively and quantitatively the so called resonating valence bond in realistic materials, by improving standard ab initio calculations by means of quantum Monte Carlo methods. In this framework we clearly identify the Kekule and Dewar contributions to the chemical bond of the benzene molecule, and we establish the corresponding resonating valence bond energy of these well known structures ($simeq 0.01$eV/atom). We apply this method to unveil the nature of the chemical bond in undoped graphene and show that this picture remains only within a small resonance length of few atomic units.
We have performed Diffusion Quantum Monte Carlo simulations of Li clusters showing that Resonating-Valence-Bond (RVB) pairing correlations between electrons provide a substantial contribution to the cohesive energy. The RVB effects are identified in terms of electron transfers from s- to p-like character, constituting a possible explanation for the breakdown of the Fermi liquid picture observed in recent high resolution Compton scattering experiments for bulk Li.
Dickes original thought experiment with two spins coupled to a photon mode has recently been experimentally realized. We propose extending this experiment to N spins and show that it naturally gives rise to highly entangled states. In particular, it gives rise to dark states which have resonating valence bond (RVB) character. We first consider a system of N two level spins in a cavity with only one spin in the excited state. This initial state is a linear combination of a dark state and a bright state. We point out the dark state is a coherent superposition of singlets with resonating valence bond character. We show that the coupling to the photon mode takes the spin system into a mixed state with an entangled density matrix. We next consider an initial state with half of the spins in the excited state. We show that there is a non-zero probability for this to collapse into a dark state with RVB character. In the lossy cavity limit, if no photon is detected within several decay time periods, we may deduce that the spin system has collapsed onto the dark RVB state. We show that the probability for this scales as 2/N, making it possible to generate RVB states of 20 spins or more.
The Kagome Heisenberg antiferromagnet is mapped onto an effective Hamiltonian on the star superlattice by Contractor Renormalization. Comparison of ground state energies on large lattices to Density Matrix Renormalization Group justifies truncation of effective interactions at range 3. Within our accuracy, magnetic and translational symmetries are not broken (i.e. a spin liquid ground state). However, we discover doublet spectral degeneracies which signal the onset of p6 - chirality symmetry breaking. This is understood by simple mean field analysis. Experimentally, the p6 chiral order parameter should split the optical phonons degeneracy near the zone center. Addition of weak next to nearest neighbor coupling is discussed.
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