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arXiv:cond-mat/9512044

Ferromagnetism in the Hubbard Model on the Infinite Dimensional fcc Lattice

M. Ulmke

Published Dec 6, 1995• 0 citations
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Abstract

The Hubbard model on the fcc lattice is studied in the limit of infinite spatial dimensions. At sufficiently strong interaction finite temperature Quantum Monte Carlo calculations yield a second order phase transition to a highly polarized ferromagnetic state. Ferromagnetism is stable over a wide hole doping regime but not for electron doping. A possible non-Fermi liquid behavior is discussed.

DOI
10.48550/arxiv.cond-mat/9512044

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The Hubbard model on the fcc lattice is studied in the limit of infinite spatial dimensions. At sufficiently strong interaction finite temperature Quantum Monte Carlo calculations yield a second order phase transition to a highly polarized ferromagnetic state. Ferromagnetism is stable over a wide hole doping regime but not for electron doping. A possible non-Fermi liquid behavior is discussed.
We present different numerical calculations based on variational quantum Monte Carlo simulations supporting a ferromagnetic ground state for finite and small hole densities in the two-dimensional infinite-U Hubbard model. Moreover, by studying the energies of different total spin sectors, these calculations strongly suggest that the paramagnetic phase is unstable against a phase with a partial polarization for large hole densities delta approximately 0.40 with evidence for a second-order transition to the paramagnetic large doping phase.
Two-dimensional Hubbard lattices with two or three holes are investigated as a function of UUU in the large-UUU limit. In the so-called Nagaoka limit (one-hole system at infinite UUU), it is known that the Hubbard model exhibits a ferromagnetic ground state. Here, by means of exact full configuration interaction quantum Monte Carlo simulations applied to periodic lattices up to 24 sites, we compute spin-spin correlation functions as a function of increasing UUU. The correlation functions clearly demonstrate the onset of ferromagnetic domains, centered on individual holes. The overall total spin of the wave functions remains the lowest possible (0 or 12\frac{1}{2}21​, depending on the number of holes). The ferromagnetic domains appear at interaction strengths comparable to the critical interaction strengths of the Nagaoka transition in finite systems with strictly one hole. The existence of such ferromagnetic domains is the signature of Nagaoka physics in Hubbard systems with a small (but greater than 1) number of holes.
Using a quantum Monte Carlo technique, we provide strong evidence for the stability of a saturated ferromagnetic phase in the high-density regime of the two-dimensional infinite-UUU Hubbard model. By decreasing the electron density, we observe a discontinuous transition to a paramagnetic phase, accompanied by a divergence of the susceptibility on the paramagnetic side. This behavior, resulting from a high degeneracy among different spin sectors, is consistent with an infinite-order phase transition. The remarkable stability of itinerant ferromagnetism renews the hope of describing this phenomenon within a purely kinetic mechanism and will facilitate the validation of experimental quantum simulators with cold atoms loaded in optical lattices.
The infinite-dimensional Hubbard model is studied by means of a modified perturbation theory. The approach reduces to the iterative perturbation theory for weak coupling. It is exact in the atomic limit and correctly reproduces the dispersions and the weights of the Hubbard bands in the strong-coupling regime for arbitrary fillings. Results are presented for the hypercubic and an fcc-type lattice. For the latter we find ferromagnetic solutions. The filling-dependent Curie temperature is compared with the results of a recent quantum Monte Carlo study.
It is shown that the dynamics of a single $\ensuremath{\downarrow}$-electron interacting with a band of $\ensuremath{\uparrow}$-electrons can be calculated exactly in the limit of infinite dimension. The corresponding Green function is determined as a continued fraction. It is used to investigate the stability of saturated ferromagnetism and the nature of the ground state for two generic nonbipartite infinite dimensional lattices. Non-Fermi-liquid behavior is found. For certain dopings the $\ensuremath{\downarrow}$-electron is bound to the $\ensuremath{\uparrow}$-holes.
We study the Hubbard model in dimension d= infinity , within an approximation that simultaneously reproduces the atomic limit and the weak-coupling limit up to second order in the interaction strength U. This method, which is a slightly modified version of an approximation suggested by Edwards and Hertz, is applied to the calculation of the self-energy and of the spectral function in the paramagnetic regime for different U, band fillings n, and temperatures T. We find Fermi-liquid behaviour for small U and (for half-filling n=0.5) a metal-insulator (Mott) transition at a critical value U cr , but also a metallic non-Fermi-liquid phase for intermediate values U<U cr . We compare our results with results obtained within the second-order perturbation theory in U and (at finite temperature) with the (essentially exact) quantum Monte Carlo (QMC) results. Qualitatively, the approximation reproduces the correct tendencies obtained by QMC, but in detail there are still discrepancies, in particular for intermediate values of U.