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Physical review. B, Condensed matter

Holes in the infinite-UHubbard model: Instability of the Nagaoka state

Yan Yan Fang, Andrei E. Ruckenstein, Elbio R. Dagotto, Stefan Schmitt-Rink

Published Oct 1, 1989• 79 citations
Publisher

Abstract

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.

DOI
10.1103/physrevb.40.7406

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Modern Physics Letters B•Oct 30, 1993•0 citations
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.
Ferromagnetic domains in the large-UUU Hubbard model with a few holes: an FCIQMC study
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 FCIQMC 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, centred on individual holes. The overall total spin of the wavefunctions remain 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 one) number of holes.
The infinite-U Hubbard model on finite two-dimensional square lattices is investigated by the use of exact numerical diagonalization. Configurations with one spin flip away from the ferromagnetic state and up to three holes are studied for lattice sizes ranging from 4*4 to 12*12. For all these situations, the state with one spin flip is found to be more stable than the Nagaoka ferromagnetic state. The crystal momentum of the ground state in this spin sector depends on the system size. Systematic comparison with the Gutzwiller wavefunction shows that it reproduces qualitatively the crystal momentum dependence of the energy, but not the exact correlation between the spin flip and the holes.
In this paper, we have rigorously shown that, in a thermodynamic limit, there always exists a one-spin-flipped state degenerate with the Nagaoka state in one-band Hubbard model on a two and three-dimensional simple cubic lattice when the number of holes [Formula: see text] (with 0≤α<1, N∧ and N e are the numbers of sites and electrons respectively) for all U (including U=∞). It is also shown that there does not exist a finite critical value U c for which, when U>U c , the Nagaoka state has the ground-state energy of the system for a two-dimensional square lattice when ρ→0.