Abstract
One flipped spin in the spin-polarized sector of the Hubbard model away from half-filling is considered. Aspects other than stability of the Nagaoka solution or viability of the Gutzwiller approximation (considered previously by other authors) are focused on. It is argued that understanding the phase-coherence properties of the flipped spin may be a good starting point in an attempt to prove or disprove the violation of the Fermi-liquid-like behavior in the two-dimensional (2D) Hubbard model, an outcome that has been strongly advocated by P. W. Anderson. The system is analyzed in the weak-coupling limit via a variational wave function in 1D and 2D. The variational problem is reduced to solving a nonlinear Schr\"odinger equation in both of these dimensionalities. It is found that a solitonic type of solution emerges in weak coupling in 1D, but not in 2D. This implies a conventional Fermi-liquid-like behavior in our system in 2D in the weak-coupling limit. A discussion of possible loopholes in our approach is presented, and the remaining possibility of non-Fermi-liquid-like behavior in the strong-coupling limit at finite densities in 2D is noted. An interesting connection with the existing work on heavy mobile impurities in metals and in $^{3}\mathrm{He}$ is pointed out.
Published Version
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