Kagomé Lattice Antiferromagnet Stripped to Its Basics

P. Azaria; C. Hooley; P. Lecheminant; C. Lhuillier; A. M. Tsvelik

doi:10.1103/PhysRevLett.81.1694

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Kagomé Lattice Antiferromagnet Stripped to Its Basics

P. Azaria¹, C. Hooley², P. Lecheminant³, C. Lhuillier¹, and A. M. Tsvelik²

¹Laboratoire de Physique Théorique des Liquides, Université Pierre et Marie Curie, 4 Place Jussieu, 75252 Paris, France
²Department of Physics, University of Oxford, 1 Keble Road, Oxford OX1 3NP, United Kingdom
³Laboratoire de Physique Théorique et Modélisation, Université de Cergy-Pontoise, Site de Saint Martin, 2 avenue Adolphe Chauvin, 95302 Cergy-Pontoise Cedex, France

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Phys. Rev. Lett. 81, 1694 – Published 24 August, 1998

DOI: https://doi.org/10.1103/PhysRevLett.81.1694

Abstract

We study a model of the spin $S = 1 / 2$ Heisenberg antiferromagnet on a one-dimensional lattice with the local symmetry of the two-dimensional Kagomé lattice. Using three complementary approaches, it is shown that the low-energy spectrum can be described by two critical Ising models with different velocities. One of these velocities is small, leading to a strongly localized Majorana fermion. These excitations are singlet ones, whereas the triplet sector has a spectral gap.

Comments & Replies

Azaria et al. Reply:

P. Azaria, C. Hooley, P. Lecheminant, C. Lhuillier, and A. M. Tsvelik

Phys. Rev. Lett. 85, 3331 (2000)

Comment on “Kagomé Lattice Antiferromagnet Stripped to Its Basics”

Steven R. White and Rajiv R. P. Singh

Phys. Rev. Lett. 85, 3330 (2000)

References (13)

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C. Zeng and V. Elser, Phys. Rev. B 42, 8436 (1990); J. T. Chalker and J. F. G. Eastmond, 46, 14 201 (1992); R. R. P. Singh and D. A. Huse, Phys. Rev. Lett. 68, 1766 (1992); S. Sachdev, Phys. Rev. B 45, 12 377 (1992); P. W. Leung and V. Elser, 47, 5459 (1993).
P. Lecheminant, B. Bernu, C. Lhuillier, L. Pierre, and P. Sindzingre, Phys. Rev. B 56, 2521 (1997).
N. Elstner and A. P. Young, Phys. Rev. B 50, 6871 (1994).
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D. G. Shelton, A. A. Nersesyan, and A. M. Tsvelik, Phys. Rev. B 53, 8521 (1996); D. Allen and D. Sénéchal, 55, 299 (1997).
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[c1] J. T. Chalker, P. C. W. Holdsworth, and E. F. Shender, Phys. Rev. Lett. 68, 855 (1992); A. B. Harris, C. Kallin, and A. J. Berlinsky, Phys. Rev. B 45, 2899 (1992); A. Chubukov, Phys. Rev. Lett. 69, 832 (1992); P. Chandra, P. Coleman, and I. Ritchey, J. Phys. I (France) 3, 591 (1993).

[c2] C. Zeng and V. Elser, Phys. Rev. B 42, 8436 (1990); J. T. Chalker and J. F. G. Eastmond, 46, 14 201 (1992); R. R. P. Singh and D. A. Huse, Phys. Rev. Lett. 68, 1766 (1992); S. Sachdev, Phys. Rev. B 45, 12 377 (1992); P. W. Leung and V. Elser, 47, 5459 (1993).

[c3] P. Lecheminant, B. Bernu, C. Lhuillier, L. Pierre, and P. Sindzingre, Phys. Rev. B 56, 2521 (1997).

[c4] N. Elstner and A. P. Young, Phys. Rev. B 50, 6871 (1994).

[c5] G. Sierra, J. Phys. A 29, 3299 (1996).

[c6] I. Affleck, Nucl. Phys. B265, 409 (1986).

[c7] A. B. Zamolodchikov and V. A. Fateev, Sov. J. Nucl. Phys. 43, 657 (1986).

[c8] D. G. Shelton, A. A. Nersesyan, and A. M. Tsvelik, Phys. Rev. B 53, 8521 (1996); D. Allen and D. Sénéchal, 55, 299 (1997).

[c9] V. J. Emery and S. A. Kivelson, Phys. Rev. B 46, 10 812 (1992).

[c10] E. H. Rezayi and J. Sak, Phys. Lett. 89A, 451 (1982).

[c11] O. Zachar, S. A. Kivelson, and V. J. Emery, Phys. Rev. Lett. 77, 1342 (1996); P. Coleman, A. Georges, and A. M. Tsvelik, J. Phys. Condens. Matter 9, 345 (1997).

[c12] A. M. Tsvelik, Phys. Rev. Lett. 69, 2142 (1992); P. Coleman, E. Miranda, and A. M. Tsvelik, Phys. Rev. B 49, 8955 (1994).

[c13] P. Coleman, L. B. Ioffe, and A. M. Tsvelik, Phys. Rev. B 52, 6611 (1995).

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Kagomé Lattice Antiferromagnet Stripped to Its Basics

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