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Physical review. B, Condensed matter

Numerical simulation of the resonant valence-bond state

J. Callaway

Published Jun 1, 1987• 47 citations
Publisher

Abstract

The resonant valence-bond state, proposed by Anderson as a possible ground state in certain antiferromagnetic systems, and relevant to the problem of high-temperature superconductivity, is studied by numerical simulation on a finite cluster. It is found to be the ground state of a simple Hubbard model with a half-filled band on a centered hexagon for a range of intermediate values of the electron interaction parameter. A singlet ground state is obtained away from the half-filled limit for the same parameters.

DOI
10.1103/physrevb.35.8723

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The resonant valence-bond state, proposed by Anderson as a possible ground state in certain antiferromagnetic systems, and relevant to the problem of high-temperature superconductivity, is studied by numerical simulation on a finite cluster. It is found to be the ground state of a simple Hubbard model with a half-filled band on a centered hexagon for a range of intermediate values of the electron interaction parameter. A singlet ground state is obtained away from the half-filled limit for the same parameters.
The one-dimensional Hubbard model with first- and second-neighbor hopping, t1 and t2, with t2≊t1/(2)1/2 and large repulsion U, is proposed as a testing ground of Anderson’s idea that the existence of an resonating valence bond ground state in the half-filled-band case will show superconductivity when a finite concentration of holes is introduced. Interestingly, our preliminary calculations in the U=∞ limit for small chains have revealed a new mechanism for enhancement of singlet pairing: We find that for t2<0 the ground state is a singlet, and, for t2<0 and ‖t2/t1‖≪1, the nearest-neighbor extended-singlet-pairing correlation function becomes enhanced appreciably as the temperature decreases below t2.
Gutzwiller variational method is applied to an effective two-dimensional Hubbard model to examine the recently proposed gossamer superconductor by Laughlin (LANL cond-mat/0209269). The ground state at half filled electron density is a gossamer superconductor for smaller intrasite Coulomb repulsion U and a Mott insulator for larger U. The gossamer superconducting state is similar to the resonating valence bond superconducting state, except that the chemical potential is approximately pinned at the mid of the two Hubbard bands away from the half filled.
We have calculated the energy of the resonating-valence-bond (RVB) state made of nearest-neighbor singlet pairs in the two-dimensional Hubbard model at half filling and the energy of holes in the RVB state near half filling. The energy of the RVB state was obtained by extrapolating the result in a 6\ifmmode\times\else\texttimes\fi{}6 square lattice with the periodic boundary condition to the infinite lattice. The energy of holes was obtained by examining the first five moments of the density of states of holes in the RVB state. We find that the holes are more stabilized in the RVB state than in the N\'eel state for J/t\ensuremath{\gtrsim}0.1, where J and t are the exchange interaction and the nearest-neighbor hopping integral, respectively. We discuss the possibility of the RVB state in the high-Tc{T}_{c}Tc​ Cu oxides.
We report on a numerical study of the two-dimensional Hubbard model and describe two new algorithms for the simulation of many-electron systems. These algorithms allow one to carry out simulations within the grand canonical ensemble at significantly lower temperatures than had previously been obtained and to calculate ground-state properties with fixed numbers of electrons. We present results for the two-dimensional Hubbard model with half- and quarter-filled bands. Our results support the existence of long-range antiferromagnetic order in the ground state at half-filling and its absence at quarter-filling. Results for the magnetic susceptibility and the momentum occupation along with an upper bound to the spin-wave spectrum are given. We find evidence for an attractive effective d-wave pairing interaction near half-filling but have not found evidence for a phase transition to a superconducting state.
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.