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Physical review. B, Condensed matter

Perturbative and variational calculations of charge fluctuations of an extended Hubbard model

S. N. Coppersmith, P. B. Littlewood

Published Feb 1, 1990• 14 citations
Publisher

Abstract

A charge-transfer instability that occurs in an extended Hubbard model with strong nearest-neighbor repulsions is examined nonperturbatively using variational wave functions. We show that a single mode approximation applied to a Hartree-Fock wave function accurately reproduces previous weak-coupling results on excitonic spectra. We then apply the method to a Gutzwiller variational wave function and extract information about the dynamic charge fluctuations in the intermediate and strong-coupling regimes.

DOI
10.1103/physrevb.41.2646

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A charge-transfer instability that occurs in an extended Hubbard model with strong nearest-neighbor repulsions is examined nonperturbatively using variational wave functions. We show that a single mode approximation applied to a Hartree-Fock wave function accurately reproduces previous weak-coupling results on excitonic spectra. We then apply the method to a Gutzwiller variational wave function and extract information about the dynamic charge fluctuations in the intermediate and strong-coupling regimes.
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We study the spin and charge fluctuations of the extended Hubbard model with on-site interaction UUU and first neighbor interaction VVV on the two-dimensional square lattice in the weak to intermediate coupling regime. We propose an extension of the two-particle self-consistent approximation that includes the effect of functional derivatives of the pair-correlation functions on irreducible spin and charge vertices. These functional derivatives were ignored in our previous work. We evaluate them assuming particle-hole symmetry. The resulting theory satisfies conservation laws and the Mermin-Wagner theorem. Our current results are in much better agreement with benchmark quantum Monte Carlo results. This theory allows us to reliably determine the crossover temperatures toward renormalized-classical regimes, and hence, the dominant instability as a function of UUU and VVV. We have considered fillings n=1n=1n=1 and n=0.75n=0.75n=0.75. Either spin or charge fluctuations can dominate. The wave vector is self-determined by the approach.
Exact diagonalisations of the extended two-band Hubbard model are performed. In the insulating regime it is shown that the nearest-neighbour copper-oxygen repulsion, V , leads to Frenkel excitons in the charge transfer gap at values of V of the order of copper-oxygen hybridisation, t . In the metallic regime it is shown that the static charge transfer and density-density correlation functions diverge as a function of V , indicating a charge transfer instability and phase separation. This is accompanied by a softening of the q → 0 mode of the dynamic correlation functions which is associated with the excitonic excitations responsible for the superconducting correlations observed in the proximity of the phase separation boundary described by C. Vermeulen et al. (C. Vermeulen et al. , Europhys. Lett. , 28 (1994) 653).
We investigate charge fluctuations in the two-dimensional Hubbard model as a function of doping, interaction strength, next-nearest-neighbor hopping, and temperature within the eight-site dynamical cluster approximation. In the regime of intermediate interaction strengths, we find that ddd density wave fluctuations, which had previously been postulated using analytical arguments, are present and strong but cannot be interpreted as the cause of the pseudogap in the model, due to their evolution with doping and interaction strength. For all parameters away from half filling, the charge fluctuations investigated, including ddd density wave fluctuations, are weaker than ddd-wave superconducting fluctuations.
We present a method to compute pairing fluctuations on top of the Gutzwiller approximation (GA). Our investigations are based on a charge-rotational invariant GA energy functional which is expanded up to second order in the pair fluctuations. Equations of motion for the fluctuations lead to a renormalized ladder-type approximation. Both spectral functions and corrections to static quantities, such as the ground-state energy, are computed. The quality of the method is examined for the single-band Hubbard model, where we compare the dynamical pairing correlations for sss- and ddd-wave symmetries with exact diagonalizations. We find a significant improvement with respect to analogous calculations done within the standard Hartree-Fock ladder approximation. The technique has potential applications in the theory of Auger spectroscopy, superconductivity, and cold atom physics.