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Physical review. B, Condensed matter

Instability of the Nagaoka state with more than one hole

Benoît Douçot, Xiao-Gang Wen

Published Aug 1, 1989• 117 citations
Publisher

Abstract

The infinite-U Hubbard model with a finite number of holes is studied. With two holes, the Nagaoka state is shown not to be the ground state of the model in any dimensions. The one-dimensional model with an arbitrary number of holes is also studied in detail.
DOI
10.1103/physrevb.40.2719

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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.
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.