A renormalised Hamiltonian approach to a resonant valence bond wavefunction

Abstract

The effective Hamiltonian of strongly correlated electrons on a square lattice is replaced by a renormalised Hamiltonian and the factors that renormalize the kinetic energy of holes and the Heisenberg spin-spin coupling are calculated using a Gutzwiller approximation scheme. The accuracy of this renormalization procedure is tested numerically and found to be qualitatively excellent. Within the scheme a resonant valence bond (RVB) wavefunction is found at half-filling to be lower in energy than the antiferromagnetic state. If the wavefunction is expressed in fermion operators, local SU(2) and U(l) invariance leads to a redundancy in the representation. The introduction of holes removes these local invariances and we find that a d-wave RVB state is lowest in energy. This state has a superconducting order parameter whose amplitude is linear in the density of holes.

Possible effects of charge frustration inNaxCoO2: Bandwidth suppression, charge orders, and resurrected resonating valence bond superconductivity

“…It is possible to perform essentially exact evaluations of the expectation values with such fermionic wavefunctions using a well established and documented Variational Monte Carlo (VMC) procedure. 21,22,25 Such detailed studies of the tV energetics at experimentally relevant x = 0.7 and 0.35 are reported in the next section.…”

“…Useful and fairly accurate guidance is obtained through the following "renormalized meanfield" procedure, 20, 21,22 which is much simpler computationally and is also more amenable to interpretation and extrapolation in the regime where VMC results become inconclusive. Generalization of the configuration counting arguments mentioned earlier leads to the following estimate of the hopping energy renormalization in the JG wavefunction relative to the unprojected free fermion wavefunction:…”

“…We formulate this meanfield as an approximate variational procedure. 21,22,26 This is particularly convenient for the present work, which also takes the variational wavefunction perspective.…”

Bosonic resonating valence bond wave function for doped Mott insulators

“…In conventional slave particle decompositions, the constraint reduces to a single occupancy constraint like (4), and is still difficult to treat. Typically, the constraint is relaxed at the level of mean field theory, and restoring its effect beyond the mean field theory (say, by a gauge theory) is a very challenging problem.…”

“…Clearly, an exact ψ b would satisfy the single occupancy constraint (4). But, the point is that an approximate ψ b determined without the constraint does not affect ψ e , owing to K. It means that in the phase string representation the constraint (4) is indeed "unimportant", which may be understood in the following way.…”