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Europhysics Letters (EPL)

2 e or not 2 e : Flux Quantization in the Resonating Valence Bond State

Steven Allan Kivelson, Daniel S. Rokhsar, James P. Sethna

Published Jun 15, 1988• 29 citations
Publisher

Abstract

The "resonating valence bond" (RVB) state has been proposed as the basis for an explanation of high-temperature superconductivity. Recently, we have described the charge and spin excitations about this state, and have shown that they are solitons, precisely analogous to those found in polyacetylene. Since the charged solitons are + e bosons, it is natural to ask whether flux quantization will occur in units of hc /2 e , as in traditional BCS superconductivity, or will come only in larger units of hc/e . We show here that flux quantization in units of hc /2 e will occur unless a condensation of cooperative ring exchanges occurs analogous to that found in the fractional quantized Hall effect.

DOI
10.1209/0295-5075/6/4/013

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The "resonating valence bond" (RVB) state has been proposed as the basis for an explanation of high-temperature superconductivity. Recently, we have described the charge and spin excitations about this state, and have shown that they are solitons, precisely analogous to those found in polyacetylene. Since the charged solitons are + e bosons, it is natural to ask whether flux quantization will occur in units of hc /2 e , as in traditional BCS superconductivity, or will come only in larger units of hc/e . We show here that flux quantization in units of hc /2 e will occur unless a condensation of cooperative ring exchanges occurs analogous to that found in the fractional quantized Hall effect.
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 UUU from a Gossamer superconductor at small UUU. At the critical value U=UcU={U}_{c}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>UcU>{U}_{c}U>Uc​ to a Gossamer SC state at U<UcU<{U}_{c}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.
We present a formulation of the resonating-valence-bond theory of the large-UUU one-band Hubbard model in two dimensions, in which the correlated ground state of the system is represented as a fluid of mobile singlet bonds. We describe this fluid as a quantum fluid of interacting hardcore bosons, and a ground-state wave function for the interacting bosons is studied in which two-body correlations are introduced by applying techniques previously developed in Laughlin's theory of the fractional quantum Hall problem. The resulting many-particle state in this formulation exhibits an incipient momentum space condensation and a class of particlelike excitations in the form of quantized vortices which possess fractional particle number, and interesting dynamics. Application of this model to the doped state reveals a mechanism by which the electrostatic repulsive interactions between the charged quasiparticles in the doped fluid stabilize the resonating state relative to the doped N\'eel state at discrete well-correlated "commensurate" hole concentrations. A superconducting state in this doped fluid arises from a condensation which pairs the charged quasiparticles; it is identified as the most stable of a hierarchy of possible condensed quasiparticle states. The condensed state exhibits many properties associated with conventional superconductivity, including dissipationless flow of current, Meissner effect, and flux quantization in units of hc2e\frac{\mathrm{hc}}{2e}2ehc​.
Resonating valence bond (RVB) states are of crucial importance in our intuitive understanding of quantum spin liquids in 2D. We systematically classify short-range bosonic RVB states into symmetric or nematic spin liquids by examining their flux patterns. We further map short-range bosonic RVB states into projected BCS wave functions, on which we perform large-scale Monte Carlo simulations without the minus sign problem. Our results clearly show that both spin and dimer correlations decay exponentially in all the short-range frustrated (nonbipartite or Z2) bosonic RVB states we studied, indicating that they are gapped Z2 quantum spin liquids. Generically, we conjecture that all short-range frustrated bosonic RVB states in 2D have only short-range correlations.
Resonating valence bond (RVB) states are of crucial importance in our intuitive understanding of quantum spin liquids in 2D. We systematically classify short-range bosonic RVB states into symmetric or nematic spin liquids by examining their flux patterns. We further map short-range bosonic RVB states into projected BCS wave functions, on which we perform large-scale Monte Carlo simulations without the minus sign problem. Our results clearly show that both spin and dimer correlations decay exponentially in all the short-range frustrated (non-bipartite or Z2Z_2Z2​) bosonic RVB states we studied, indicating that they are gapped Z2Z_2Z2​ quantum spin liquids. Generically, we conjecture that all short-range frustrated bosonic RVB states in 2D have only short-range correlations.