Resonating valence bond theory

Summary

In condensed matter physics, the resonating valence bond theory (RVB) is a theoretical model that attempts to describe high-temperature superconductivity, and in particular the superconductivity in cuprate compounds. It was first proposed by an American physicist P. W. Anderson and Indian theoretical physicist Ganapathy Baskaran in 1987. The theory states that in copper oxide lattices, electrons from neighboring copper atoms interact to form a valence bond, which locks them in place. However, with doping, these electrons can act as mobile Cooper pairs and are able to superconduct. Anderson observed in his 1987 paper that the origins of superconductivity in doped cuprates was in the Mott insulator nature of crystalline copper oxide. RVB builds on the Hubbard and t-J models used in the study of strongly correlated materials. In 2014, evidence showing that fractional particles can happen in quasi two-dimensional magnetic materials, was found by EPFL scientists lending support for Anderso

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https://en.wikipedia.org/wiki/Resonating_valence_bond_theory

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This thesis is devoted to a theoretical study of high-temperature superconductivity from the viewpoint of a doped Mott insulator. To this end, the square-lattice t-J model is analyzed by variational and mean-field approaches. The thesis focuses on the construction of excitations and on spectral properties in the framework of Anderson's concept of resonating-valence-bond wavefunctions. The quantum dimer model as a toy model for the resonating-valence-bond phase of Mott insulators is also explored. In the first part of the thesis, the single-particle Green's functions in the superconducting phase are analyzed using Gutzwiller-projected variational wavefunctions for the t-J model. It is found that the overall spectral weight is reduced by a momentum-dependent renormalization, and that the projection produces a particle-hole asymmetry in the renormalization of the spectral weights. The second part analyzes the Green's functions in the pseudogap phase of the cuprates within an SU(2) mean-field approach where the order parameter fluctuates between the d-wave superconductor and the non-superconducting staggered-flux state. The model predicts a photoemission spectrum with an asymmetric gap structure interpolating between the superconducting gap centered at the Fermi energy and the asymmetric staggered-flux gap. This gap asymmetry changes sign at the "hot-spots" where the Fermi surface crosses the diagonal (0,π)-(π,0). In the last part of the thesis, single hole and vortex excitations in the liquid phase of the triangular-lattice Rokhsar-Kivelson quantum dimer model are considered. It is found that the motion of a hole bound to a topological excitation is strongly constrained due to interference effects.

EPFL2008

SU(4) topological resonating valence bond spin liquid on the square lattice

Olivier Clément Romain Gauthé

We generalize the construction of the spin-1/2 SU(2) resonating valence bond (RVB) state to the case of the self-conjugate 6 representation of SU(4). As for the case of SU(2) [J.-Y. Chen and D. Poilblanc, Phys. Rev. B 97, 161107(R) (2018)], we use the projected entangled pair state (PEPS) formalism to derive a simple (two-dimensional) family of generalized SU(4) RVB states on the square lattice. We show that, when longer-range SU(4)-singlet bonds are included, a local gauge symmetry is broken down from U(1) to Z(2), leading to the emergence of a short-range spin liquid. Evidence for the topological nature of this spin liquid is provided by the investigation of the Renyi entanglement entropy of infinitely long cylinders and of the modular matrices. Relevance to microscopic models and experiments of ultracold atoms is discussed.

2019

Identification of an RVB liquid phase in a quantum dimer model with competing kinetic terms

Frédéric Mila, François Vernay

Starting from the mean-field solution of a spin-orbital model of LiNiO2, we derive an effective quantum dimer model (QDM) that lives on the triangular lattice and contains kinetic terms acting on four-site plaquettes and six-site loops. Using exact diagonalizations and Green’s function Monte Carlo simulations, we show that the competition between these kinetic terms leads to a resonating valence bond (RVB) state for a finite range of parameters. We also show that this RVB phase is connected to the RVB phase identified in the Rokhsar-Kivelson model on the same lattice in the context of a generalized model that contains both the six-site loops and a nearest-neighbor dimer repulsion. These results suggest that the occurrence of an RVB phase is a generic feature of QDM with competing interactions.

2006