Modern Physics Letters B

VARIATIONAL STUDY ON INSTABILITY OF NAGAOKA STATE IN A THERMODYNAMIC LIMIT

Shun-Qing Shen, Zhaoming Qiu

Published Oct 30, 1993• 0 citations

Abstract

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.

DOI: 10.1142/s0217984993001648

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Modern Physics Letters B

VARIATIONAL STUDY ON INSTABILITY OF NAGAOKA STATE IN A THERMODYNAMIC LIMIT

Shun-Qing Shen, Zhaoming Qiu

Published Oct 30, 1993• 0 citations

Publisher

Abstract

DOI: 10.1142/s0217984993001648

Related papers

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We discuss the stability of the saturated ferromagnetic state of the one-band Hubbard model in the thermodynamic limit. We prove rigorously that the Nagaoka state is stable on a d-dimensional (d=2,3) simple-cubic lattice if the number of holes ${\mathit{N}}_{\mathit{h}}$ is less than ${\mathit{N}}_{\mathrm{\ensuremath{\Lambda}}}^{\mathrm{\ensuremath{\alpha}}}$, 0\ensuremath{\le}\ensuremath{\alpha}1/2d. Finally, we explain briefly why the Nagaoka state is probably unstable when ${\mathit{N}}_{\mathit{h}}$ \ensuremath{\gg}${\mathit{N}}_{\mathrm{\ensuremath{\Lambda}}}^{1/2\mathit{d}}$.We discuss the stability of the saturated ferromagnetic state of the one-band Hubbard model in the thermodynamic limit. We prove rigorously that the Nagaoka state is stable on a d-dimensional (d=2,3) simple-cubic lattice if the number of holes ${\mathit{N}}_{\mathit{h}}$ is less than ${\mathit{N}}_{\mathrm{\ensuremath{\Lambda}}}^{\mathrm{\ensuremath{\alpha}}}$, 0\ensuremath{\le}\ensuremath{\alpha}1/2d. Finally, we explain briefly why the Nagaoka state is probably unstable when ${\mathit{N}}_{\mathit{h}}$\ensuremath{\gg}${\mathit{N}}_{\mathrm{\ensuremath{\Lambda}}}^{1/2\mathit{d}}$.

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{\mathit{N}}_{\mathit{h}}

is less than ${\mathit{N}}_{\mathrm{\ensuremath{\Lambda}}}^{\mathrm{\ensuremath{\alpha}}}$, 0\ensuremath{\le}\ensuremath{\alpha}1/2d. Finally, we explain briefly why the Nagaoka state is probably unstable when

{\mathit{N}}_{\mathit{h}}

\ensuremath{\gg}${\mathit{N}}_{\mathrm{\ensuremath{\Lambda}}}^{1/2\mathit{d}}$.

Ferromagnetic domains in the large-

U

Hubbard model with a few holes: an FCIQMC study

Two-dimensional Hubbard lattices with two or three holes are investigated as a function of

U

in the large-

U

limit. In the so-called Nagaoka limit (one-hole system at infinite

U

), 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

U

. 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

\frac{1}{2}

, 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.