Ferromagnetism in the Two Dimensional <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>t</mi><mo>−</mo><mrow><msup><mrow><mi>t</mi></mrow><mrow><mo>′</mo></mrow></msup></mrow></math></span> Hubbard Model at the Van Hove Density

R. Hlubina; S. Sorella; F. Guinea

doi:10.1103/PhysRevLett.78.1343

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Ferromagnetism in the Two Dimensional $t - t^{'}$ Hubbard Model at the Van Hove Density

R. Hlubina¹, S. Sorella¹, and F. Guinea²

¹INFM, International School for Advanced Studies, Via Beirut 4, I-34014 Trieste, Italy
²Instituto de Ciencia de Materiales, Consejo Superior de Investigaciones Científicas, Cantoblanco, 28049 Madrid, Spain

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Phys. Rev. Lett. 78, 1343 – Published 17 February, 1997

DOI: https://doi.org/10.1103/PhysRevLett.78.1343

Abstract

Using an improved version of the projection quantum Monte Carlo technique, we study the square-lattice Hubbard model with nearest-neighbor hopping $t$ and next-nearest-neighbor hopping $t^{'}$ by simulation of lattices with up to $20 \times 20$ sites. For a given ${R = 2 t}^{'} / t$ , we consider that filling which leads to a singular density of states of the noninteracting problem. For repulsive interactions, we find an itinerant ferromagnet (antiferromagnet) for $R = 0.94$ ( $R = 0.2$ ). This is consistent with the prediction of the $T$ -matrix approximation, which sums the most singular set of diagrams.

References (15)

See, e.g., M. Kollar et al., Phys. Rev. B 53, 9225 (1996).
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Here the VH density is obtained on a finite lattice by filling the highest-energy wave vectors $(π, 0)$ and $(0, π)$ by two up-spin and no down-spin electrons. At such filling, there is a large number of low-magnetization closed-shell configurations.
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[c1] See, e.g., M. Kollar et al., Phys. Rev. B 53, 9225 (1996).

[c2] Y. Nagaoka, Phys. Rev. 147, 392 (1966).

[c3] T. Hanisch et al., Ann. Phys. (Leipzig) 4, 303 (1995).

[c4] A. Mielke and H. Tasaki, Commun. Math. Phys. 158, 341 (1993).

[c5] H. Q. Lin and J. E. Hirsch, Phys. Rev. B 35, 3359 (1987).

[c6] J. E. Hirsch and D. J. Scalapino, Phys. Rev. Lett. 56, 2732 (1986).

[c7] Here the VH density is obtained on a finite lattice by filling the highest-energy wave vectors $(π, 0)$ and $(0, π)$ by two up-spin and no down-spin electrons. At such filling, there is a large number of low-magnetization closed-shell configurations.

[c8] S. Rudin and D. Mattis, Phys. Lett. 110A, 273 (1985).

[c9] J. R. Engelbrecht et al., Phys. Rev. B 45, 10 135 (1992).

[c10] R. Hlubina and T. M. Rice, Phys. Rev. B 52, 13 043 (1995) R. Hlubina, 53, 11 344 (1996).

[c11] S. Sorella, Int. J. Mod. Phys. 5, 937 (1991).

[c12] See, e.g., N. Trivedi and D. M. Ceperley, Phys. Rev. B 41, 4552 (1990).

[c13] S. Sorella (unpublished).

[c14] E. Heeb and T. M. Rice, Europhys. Lett. 9, 673 (1994).

[c15] W. Kohn and J. M. Luttinger, Phys. Rev. Lett. 15, 524 (1965) J. González et al., Europhys. Lett. 34, 711 (1996).

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Ferromagnetism in the Two Dimensional $t - t^{'}$ Hubbard Model at the Van Hove Density

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Ferromagnetism in the Two Dimensional t−t′ Hubbard Model at the Van Hove Density

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Ferromagnetism in the Two Dimensional $t - t^{'}$ Hubbard Model at the Van Hove Density