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Physical review. B, Condensed matter

Infinite Ud , Up ground state of the extended Hubbard model

Robert J Gooding, Veit Elser

Published Feb 1, 1990• 21 citations
Publisher

Abstract

The renormalization of the extended Hubbard model proposed by Zhang and Rice [Phys. Rev. B 37, 3759 (1988)] that leads to the (nearest-neighbor-only) t-J model is scrutinized in the infinite correlation limit. We demonstrate that the ${U}_{d}$,${U}_{p}$\ensuremath{\rightarrow}\ensuremath{\infty} limit obtained from the extended Hubbard model does not have the same ground state as the U\ensuremath{\rightarrow}\ensuremath{\infty} extrapolation of the t-J model.

DOI
10.1103/physrevb.41.2557

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The renormalization of the extended Hubbard model proposed by Zhang and Rice [Phys. Rev. B 37, 3759 (1988)] that leads to the (nearest-neighbor-only) t-J model is scrutinized in the infinite correlation limit. We demonstrate that the Ud{U}_{d}Ud​,Up{U}_{p}Up​\ensuremath{\rightarrow}\ensuremath{\infty} limit obtained from the extended Hubbard model does not have the same ground state as the U\ensuremath{\rightarrow}\ensuremath{\infty} extrapolation of the t-J model.
We investigate the ground state of the Hubbard model in one and two dimensions. Long perturbation expansions in t/U, i.e., about the atomic limit, are computed for the ground-state energy of finite lattices with N\ensuremath{\le}10 for arbitrary electron density. We also extend the series for the one-dimensional infinite lattice by expanding the Bethe-ansatz equations. Pad\'e-approximant analysis of the series shows a distribution of singularities that varies dramatically with the electron density n. We also investigate the effect of inclusion of next-nearest-neighbor hopping. This appears to have little effect at half-filling but is significant away from half-filling.
The problem of the ground state of the electronic system in the Hubbard model for U=∞ is discussed. The author investigates the normal (singlet or nonmagnetic) N state of the electronic system over the entire range of electron densities n⩽1. It is shown that the energy of the N state ɛ 0 (1) (n) in a one-particle approximation, such as (e.g.) the extended Hartree-Fock approximation, is lower than the energy of the saturated ferromagnetic FM state ɛ FM(n) for all n. The dynamic magnetic susceptibility is calculated in the random phase approximation, and it is shown that the N state is stable over the entire range of electron densities: The static susceptibility (ω=0) does not have a band singularity in the zero-wave vector limit q→0. A formally exact representation is obtained for the mass operator of the one-particle Green’s function, and an approximation of this operator is proposed: M k(E)⋍λF(E), where λ=n(1−n)/(1−n/2)z is the kinematic interaction parameter, z is the number of nearest neighbors, and F(E) is the total single-site Green’s function. For an elliptical density of states the integral equation for F(E) is solved exactly, ad it is shown that the spectral intensity rigorously satisfies the sum rule. The calculated energy of the strongly correlated N state ɛ 0(n)<ɛ FM(n) for all n, and in light of this relationship the author discusses the hypothesis that the ground state of the system is the normal (singlet) state in the thermodynamic limit. The electron distribution function at T=0 differs significantly from the Fermi step; it is “smeared” along the entire energy spectrum, and discontinuities do not occur in the region of the chemical potential m.
Motivated by the recent experimental findings on the orbital ordering of cuprate SC, we have investigated the multi-orbital Hubbard model in the framework of Cu impurity approximation embedded in the O lattice by incorporating the 3d8^{8}8 multiplet structure coupled to a full O-2p band.Our systematic investigation on the impact of anisotropy of various parameters reveal rich phenomena in terms of the ground state (GS) weight asymmetry between x^\hat{x}x^ and y^\hat{y}y^​ directions.The numerical evidence demonstrate that the GS weight of Zhang-Rice singlet (ZRS) can be affected by the asymmetry of these parameters to distinct extent. Although the experimentally motivated asymmetric charge transfer energy only induces tiny weight difference, the asymmetric ddd-ppp hybridization can result in considerable change of the weight. Besides, the nearest-neighbor VpdV_{pd}Vpd​ has much stronger impact than the local UppU_{pp}Upp​, which stems from the nature of ZRS consisting of nearest-neighbor two holes. Our systematic exploration provide valuable knowledge on the role of the artificial symmetry breaking on the two-hole GS nature and serves as the starting point of more sophisticated many-body simulations to uncover more interesting physics of multi-orbital Hubbard model within the symmetry breaking setup.
We describe a new approach to the ground state antiferromagnetic phase of the infinite-dimensional Hubbard model. The theory recovers correctly both the strong coupling Heisenberg limit at 12\frac{1}{2}21​ filling and the t-J limit in the one-hole sector, appears applicable over a wide UUU range, and is readily extended to finite dimensions.