arXiv:cond-mat/0102249 · Physical Review Letters

Nagaoka Ferromagnetism in the Two-Dimensional Infinite- U Hubbard Model

Federico Becca, Sandro Sorella

Published Apr 9, 2001• 58 citations

Abstract

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.

DOI: 10.1103/physrevlett.86.3396

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arXiv:cond-mat/0102249 · Physical Review Letters

Nagaoka Ferromagnetism in the Two-Dimensional Infinite- U Hubbard Model

Federico Becca, Sandro Sorella

Published Apr 9, 2001• 58 citations

arXiv HTML PDF

Abstract

DOI: 10.1103/physrevlett.86.3396

Related papers

Ferromagnetic domains in the large- U Hubbard model with a few holes: A full configuration interaction quantum Monte Carlo study

Su-Jun Yun, Werner Dobrautz, Hongjun Luo +3 more

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 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 $U$ . 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 $\frac{1}{2}$ , 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 1) number of holes.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 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 $U$. 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 $\frac{1}{2}$, 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 1) number of holes.

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Quantum Monte Carlo simulations of infinitely strongly correlated fermions

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Numerical simulations of the two-dimensional $t\ensuremath{-}J$ model in the limit $J/t\ensuremath{\ll}1$ are performed for rather large systems $(N\ensuremath{\sim}10\ifmmode\times\else\texttimes\fi{}10)$ using a world-line loop algorithm. It is shown that in the one-hole case with $J=0,$ very low temperatures $(\ensuremath{\beta}t\ensuremath{\sim}2500)$ are necessary in order to reach Nagaoka's state. Full polarization becomes unstable for $J\ensuremath{\sim}{10}^{\ensuremath{-}4}t$ towards partial polarization up to $J/t\ensuremath{\lesssim}0.01.$ $J/t\ensuremath{\gtrsim}0.05$ leads to minimal spin. The two-hole case shows enhanced total spin up to the lowest attainable temperatures $(\ensuremath{\beta}t=150),$ well below those reached by other finite-temperature methods.Numerical simulations of the two-dimensional $t\ensuremath{-}J$ model in the limit $J/t\ensuremath{\ll}1$ are performed for rather large systems $(N\ensuremath{\sim}10\ifmmode\times\else\texttimes\fi{}10)$ using a world-line loop algorithm. It is shown that in the one-hole case with $J=0,$ very low temperatures $(\ensuremath{\beta}t\ensuremath{\sim}2500)$ are necessary in order to reach Nagaoka's state. Full polarization becomes unstable for $J\ensuremath{\sim}{10}^{\ensuremath{-}4}t$ towards partial polarization up to $J/t\ensuremath{\lesssim}0.01.$ $J/t\ensuremath{\gtrsim}0.05$ leads to minimal spin. The two-hole case shows enhanced total spin up to the lowest attainable temperatures $(\ensuremath{\beta}t=150),$ well below those reached by other finite-temperature methods.

arXiv:cond-mat/9707108Physical review. B, Condensed matterOct 15, 199814 citations

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 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

U

. 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

\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 1) number of holes.

We investigate Nagaoka ferromagnetism in the two-dimensional Hubbard model with one hole using the spin-adapted [

\text{SU}(2)

conserving] full configuration interaction quantum Monte Carlo method. This methodology gives us access to the ground-state energies of all possible spin states

S

of finite Hubbard lattices, here obtained for lattices up to 26 sites for various interaction strengths (

U

). The critical interaction strength,

{U}_{c}

, at which the Nagaoka transition occurs is determined for each lattice and is found to be proportional to the lattice size for the larger lattices. Below

{U}_{c}

, the overall ground states are found to favour the minimal total spin (

S=\frac{1}{2}

), and no intermediate spin state is found to be the overall ground state on lattices larger than 16 sites. However, at

{U}_{c}

, the energies of all the spin states are found to be nearly degenerate, implying that large fluctuations in total spin can be expected in the vicinity of the Nagaoka transition.

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-

U

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.

J=0,

very low temperatures $(\ensuremath{\beta}t\ensuremath{\sim}2500)$ are necessary in order to reach Nagaoka's state. Full polarization becomes unstable for $J\ensuremath{\sim}{10}^{\ensuremath{-}4}t$ towards partial polarization up to $J/t\ensuremath{\lesssim}0.01.$ $J/t\ensuremath{\gtrsim}0.05$ leads to minimal spin. The two-hole case shows enhanced total spin up to the lowest attainable temperatures $(\ensuremath{\beta}t=150),$ well below those reached by other finite-temperature methods.