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Physical review. B, Condensed matter

Resonating-valence-bond state with fermionic charges and bosonic spins: Mean-field theory

Karsten Flensberg, Per Hedegrd, Michael Brix Pedersen

Published Jul 1, 1989• 31 citations
Publisher

Abstract

We consider a representation of the Hubbard model, in which the charge carriers are fermions and the spin carriers are bosons. We show that there exists a mean-field solution with a condensate of spin singlets and we characterize the low-temperature behavior of the quasiparticles. Finally, we calculate the tunneling spectrum for a normal-metal--resonating-valence-bond (RVB) state tunnel junction and suggest the tunneling experiment as a probe of the statistics of the RVB quasiparticles.

DOI
10.1103/physrevb.40.850

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Physical review. B, Condensed matter•Jan 1, 1996•4 citations
We consider a representation of the Hubbard model, in which the charge carriers are fermions and the spin carriers are bosons. We show that there exists a mean-field solution with a condensate of spin singlets and we characterize the low-temperature behavior of the quasiparticles. Finally, we calculate the tunneling spectrum for a normal-metal--resonating-valence-bond (RVB) state tunnel junction and suggest the tunneling experiment as a probe of the statistics of the RVB quasiparticles.
A two-dimensional square-lattice Hubbard model is investigated. A slave-fermion formulation, in which the electron operator is expressed by a combination of bose operators for the spin freedom, and fermi operators for the charge freedom, is used. The phase diagram for the resonating valence bond (RVB) state is obtained. The RVB state shows long-range antiferromagnetic order at T =0, the period of which deviates from that of the commensurate Néel order as the system deviates from the half-filled case.
We propose a class of ground states for doped Mott insulators in the electron second quantization representation. They are obtained from a bosonic resonating valence bond (RVB) theory of the $t\text{\penalty1000-\hskip0pt}J$ model. At half filling, the ground state describes spin correlations of the S=1∕2S=1∕2S=1∕2 Heisenberg model very accurately. Its spin degrees of freedom are characterized by RVB pairing of spins, the size of which decreases continuously as holes are doped into the system. Charge degrees of freedom emerge upon doping and are described by twisted holes in the RVB background. We show that the twisted holes exhibit an off diagonal long range order (ODLRO) in the pseudogap ground state, which has a finite pairing amplitude, but is short of phase coherence. Unpaired spins in such a pseudogap ground state behave as free vortices, preventing superconducting phase coherence. The existence of nodal quasiparticles is also ensured by such a hidden ODLRO in the ground state, which is non-Fermi liquidlike in the absence of superconducting phase coherence. Two distinct types of spin excitations can also be constructed. The superconducting instability of the pseudogap ground state is discussed and a ddd-wave superconducting ground state is obtained. This class of pseudogap and superconducting ground states unifies antiferromagnetism, pseudogap, superconductivity, and Mott physics into a new state of matter.
We show that, in the presence of Coulomb interactions, the charge of a quasiparticle in a fully gapped superconductor is a sharp quantum observable. It follows that the familiar Bogoliubov quasiparticles are neutral, spin-1/2 fermions. Since the current-carrying collective modes are spinless, charge and spin are carried by separate excitations in a superconductor. The quantum numbers of these quasiparticles are identical to those of a spinon in a ``resonating-valence-bond'' (RVB) superconductor. This supports the notion that a RVB superconductor is simply a strong-coupling version of a BCS superconductor. We describe an experiment that would directly verify the separation of charge and spin in a bulk superconductor.
The Hubbard model in the strong-coupling regime is studied by the Kondo-lattice theory. If no symmetry is broken at a sufficiently low temperature in sufficiently low dimensions, an electron liquid is stabilized by the Fock-type exchange effect of the superexchange interaction. Since the stabilization mechanism is none other than the resonating-valence-bond (RVB) mechanism, the electron liquid is none other than an RVB electron liquid. The RVB electron liquid in the Hubbard model is adiabatically connected to the RVB spin liquid in the Heisenberg model.
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.
A systematic ``loop-gas'' formalism is developed for a general study of the resonance-valence-bond (RVB) states of a quantum antiferromagnet. At half-filling, we obtain analytic, parameter-free RVB amplitudes which reproduce virtually exact ground-state energy and spin excitation spectrum. A doped hole is then modeled by a holon-spinon pair moving on this optimized RVB background. Its energy is in excellent agreement with other estimates on the finite lattice for t/J\ensuremath{\le}1. Such a pair wave function shows a finite amplitude even at infinite separation. Spin-charge separation and vanishing quasiparticle spectral weight are discussed in this framework. \textcopyright{} 1996 The American Physical Society.