Geodesic
Lattice structure of baby skyrmions
Teoretičeskaâ i matematičeskaâ fizika, Tome 160 (2009) no. 1, pp. 69-83 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We study the zero-temperature lattice structure of baby skyrmions using a full-field numerical minimization algorithm. We place baby skyrmions inside different parallelogram unit cells and impose periodic boundary conditions. We find that the minimum energy is obtained for the hexagonal lattice and that the skyrmion splits into quarter-skyrmions in the resulting configuration. In particular, the energy is lower on the hexagonal lattice than on the well-studied rectangular lattice, where splitting into half-skyrmions is observed.
Mots-clés : baby skyrmion, skyrmion
Keywords: crystalline structure. 
@article{TMF_2009_160_1_a6,
     author = {I. Hen and M. Karliner},
     title = {Lattice structure of baby skyrmions},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {69--83},
     year = {2009},
     volume = {160},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2009_160_1_a6/}
}
TY  - JOUR
AU  - I. Hen
AU  - M. Karliner
TI  - Lattice structure of baby skyrmions
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2009
SP  - 69
EP  - 83
VL  - 160
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_2009_160_1_a6/
LA  - ru
ID  - TMF_2009_160_1_a6
ER  - 
%0 Journal Article
%A I. Hen
%A M. Karliner
%T Lattice structure of baby skyrmions
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2009
%P 69-83
%V 160
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_2009_160_1_a6/
%G ru
%F TMF_2009_160_1_a6
I. Hen; M. Karliner. Lattice structure of baby skyrmions. Teoretičeskaâ i matematičeskaâ fizika, Tome 160 (2009) no. 1, pp. 69-83. http://geodesic.mathdoc.fr/item/TMF_2009_160_1_a6/

[1] T. H. R. Skyrme, Proc. R. Soc. Lond. Ser. A, 260:1300 (1961), 127–138 ; Nucl. Phys., 31 (1962), 556–569 | DOI | MR | Zbl | DOI | MR

[2] G. S. Adkins, C. R. Nappi, E. Witten, Nucl. Phys. B, 228:3 (1983), 552–566 | DOI | MR

[3] B. M. A. G. Piette, B. J. Schoers, W. J. Zakrzewski, Z. Phys. C, 65:1 (1995), 165–174 | DOI | MR

[4] A. A. Belavin, A. M. Polyakov, Pisma v ZhETF, 22:10 (1975), 503–506

[5] S. L. Sondhi, A. Karlhede, S. A. Kivelson, E. H. Rezayi, Phys. Rev. B, 47:24 (1993), 16419–16426 | DOI

[6] N. R. Walet, T. Weidig, Full 2D numerical study of the quantum Hall skyrme crystal, arXiv: cond-mat/0106157

[7] S. M. Girvin, “The quantum Hall effect: novel excitations and broken symmetries”, Topological Aspects of Low Dimensional Systems, eds. A. Comtet, J. Jolicoeur, S. Ouvry, F. David, Springer, Berlin, 1999, 53–175 | MR | Zbl

[8] Z. F. Ezawa, Quantum Hall Effects: Field Theoretical Approach and Related Topics, World Sci., Singapore, 2000 | MR | Zbl

[9] D.-H. Lee, C. L. Kane, Phys. Rev. Lett., 64:12 (1990), 1313–1317 | DOI | MR | Zbl

[10] N. S. Manton, P. M. Sutcliffe, Topological Solitons, Cambridge Monogr. Math. Phys., Cambridge Univ. Press, Cambridge, 2004 | MR | Zbl

[11] R. A. Leese, M. Peyrard, W. J. Zakrzewski, Nonlinearity, 3:3 (1990), 773–807 | DOI | MR | Zbl

[12] B. Piette, W. J. Zakrzewski, Chaos Solitons Fractals, 5:12 (1995), 2495–2508 | DOI | MR | Zbl

[13] P. M. Sutcliffe, Nonlinearity, 4:4 (1991), 1109–1121 | DOI | MR | Zbl

[14] B. M. A. G. Piette, B. J. Schoers, W. J. Zakrzewski, Nucl. Phys. B, 439:1–2 (1995), 205–235 | DOI | MR | Zbl

[15] T. Weidig, Nonlinearity, 12:6 (1999), 1489–1503 | DOI | MR | Zbl

[16] P. Eslami, M. Sarbishaei, W. J. Zakrzewski, Nonlinearity, 13:5 (2000), 1867–1881 | DOI | MR | Zbl

[17] I. Hen, M. Karliner, Nonlinearity, 113:3 (2008), 399–408 | DOI | MR | Zbl

[18] I. Hen, M. Karliner, Phys. Rev. D, 77:5 (2008), 054009 | DOI | MR

[19] E. Braaten, S. Townsend, L. Carson, Phys. Lett. B, 235:1–2 (1990), 147–152 | DOI | MR

[20] R. A. Battye, P. M. Sutcliffe, Phys. Rev. Lett., 79:3 (1997), 363–366 | DOI

[21] N. R. Walet, Nucl. Phys. A, 606:3–4 (1996), 429–458 | DOI

[22] I. Klebanov, Nucl. Phys. B, 262:1 (1985), 133–143 | DOI | MR

[23] A. S. Goldhaber, N. S. Manton, Phys. Lett. B, 198:2 (1987), 231–234 | DOI

[24] A. D. Jackson, J. J. M. Verbaarschot, Nucl. Phys. A, 484:3–4 (1988), 419–431 | DOI

[25] M. Kugler, S. Shtrikman, Phys. Lett. B, 208:3–4 (1988), 491–494 | DOI | MR

[26] L. Castellejo, P. S. J. Jones, A. D. Jackson, J. J. M. Verbaarschot, Nucl. Phys. A, 501:4 (1989), 801–812 | DOI

[27] O. Schwindt, N. R. Walet, Europhys. Lett., 55:5 (2001), 633–639 | DOI

[28] R. S. Ward, Nonlinearity, 17:3 (2004), 1033–1040 | DOI | MR | Zbl

[29] R. J. Cova, W. J. Zakrzewski, Nonlinearity, 10:5 (1997), 1305–1317 ; Eur. Phys. J. B, 15:4 (2000), 673–678 ; Rev. Mexicana Fis., 50:5 (2005), 527–535 | DOI | MR | Zbl | DOI | MR

[30] J. Bamberg, G. Cairns, D. Kilminster, Amer. Math. Monthly, 110:3 (2003), 202–209 | DOI | MR | Zbl

[31] W. H. Kleiner, L. M. Roth, S. H. Antler, Phys. Rev. A, 133:5A (1964), A1226–A1227 | DOI | MR | Zbl

[32] R. A. Battye, P. M. Sutcliffe, Phys. Lett. B, 416:3–4 (1998), 385–391 | DOI | MR

[33] M. Hale, O. Schwindt, T. Weidig, Phys. Rev. E, 62:3 (2000), 4333–4346 | DOI

[34] L. Brey, H. A. Fertig, R. Côté, A. H. MacDonald, Phys. Rev. Lett., 75:13 (1995), 2562–2565 | DOI