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Communications in Theoretical Physics

Instability of the Negaoka States in the Thermodynamic Limit

C. C. Wan

Published Sep 15, 1994• 0 citations
Publisher

Abstract

We study the infinite Hubbard model on a square lattice. By introducing a transformation which transforms the up spin and down spin fermions into two families of bosons with phase factors, we show that the fully ferromagnetic state is not the ground state at any finite hole concentration.
DOI
10.1088/0253-6102/22/2/233

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The solution of a three-body Schr\"odinger equation (for two holes and a spin flip) shows that in the U=\ensuremath{\infty} Hubbard model the saturated ferromagnetic state with two holes is unstable (in a finite volume and for periodic boundary conditions). The ground state carries a finite momentum, and becomes degenerate with the Nagaoka state in the thermodynamic limit. This is in agreement with exact diagonalization results for small lattices where, in addition, we find that the true two-hole ground state is a singlet. As a result, our notions of ferromagnetism in the Hubbard model might need revision.
Abstract The instability of the fully polarized ferromagnetic ground state (Nagaoka state) of the Hubbard model on the square lattice is investigated. We use single spin flip variational wave functions including majority spin correlation effects and calculate spin flip energies in the thermodynamic limit. With very local wave functions and with moderate numbers of variational parameters we reproduce the best known estimate for the critical hole density δcr = 0.29 and we obtain an estimate of Ucr = 63 t for the critical coupling which is considerably better than the best estimate of Ucr = 42 t previously known. The simplicity of our wave functions makes the physical origin of the various aspects of the instability particularly transparent.
The Nagaoka $(U=\ensuremath{\infty})$ limit of the Hubbard model on a square lattice is mapped onto the itinerant-localized Kondo model at infinitely strong coupling. Such a model is well suited to perform quantum Monte Carlo (QMC) simulations to compute spin correlation functions. For periodic boundary conditions, this model is shown to exhibit no short-range ferromagnetic (FM) spin correlations at any doping $\ensuremath{\delta}\ensuremath{\ge}0.01$ and at finite temperature T=0.1t.T=0.1t.T=0.1t. Our simulations give no indication that there is a tendency towards ferromagnetic ordering in the ground state, with more than one hole. Employing on the other hand the open boundary conditions (or mixed boundary conditions) may result in the qualitatively different results for the thermodynamic limit depending on the way one chooses to approach this limit. These observations imply that the relevant thermodynamic limit remains unclear.
Abstract We discuss two single spin flip variational wave functions describing spin wave excitations which were proposed earlier by Shastry, Krishnamurthy and Anderson (SKA) and by Basile and Elser (BE), respectively, in order to investigate the instability of the fully polarized ferromagnetic state (Nagaoka state) in the infinite U Hubbard model. We calculate the energy of these variational states for the square lattice and for multiple chains. At the zone boundary in the vicinity of the point (0, π) the spin wave energy is reduced substantially by the binding of the spin up hole to the flipped down spin. For the square lattice this leads to a critical hole density of δcr = 0.407 for the SKA spin wave and of δcr = 0.322 for the BE spin wave which implies remarkable improvements in comparison to the corresponding scattering states investigated previously.