Expansions for Droplet States in the Ferromagnetic XXZ Heisenberg Chain
作者： Tom Kennedy
DOI:
关键词: Quantum mechanics 、 Eigenvalues and eigenvectors 、 Periodic boundary conditions 、 Momentum 、 Chain (algebraic topology) 、 Eigenfunction 、 Dispersion relation 、 Mathematics 、 Spins 、 Spin-½
摘要: We consider the highly anisotropic ferromagnetic spin 1/2 Heisenberg chain with periodic boundary conditions. In each sector of constant total z component spin, we develop convergent expansions for lowest band eigenvalues and eigenfunctions. These eigenstates describe droplet states in which spins essentially form a single linear can move. Our results also give expansion dispersion relation, i.e., energy as function its momentum. The methods used are from math-ph/0208026 cond-mat/0104199, this short paper should serve pedagogic introduction to those papers.
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arxiv.org参考文章(12)
Taku Matsui, On the Spectra of the Kink for Ferromagnetic XXZ Models Letters in Mathematical Physics. ,vol. 42, pp. 229- 239 ,(1997) , 10.1023/A:1007396827804
Nilanjana Datta, Tom Kennedy, Expansions for One Quasiparticle States in Spin 1/2 Systems Journal of Statistical Physics. ,vol. 108, pp. 373- 399 ,(2002) , 10.1023/A:1015713005441
Bruno Nachtergaele, Interfaces and droplets in quantum lattice models arXiv: Mathematical Physics. ,(2000)
Tohru Koma, Bruno Nachtergaele, The complete set of ground states of the ferromagnetic XXZ chains Advances in Theoretical and Mathematical Physics. ,vol. 2, pp. 533- 558 ,(1998) , 10.4310/ATMP.1998.V2.N3.A4
R. F. Werner, C. T. Gottstein, Ground states of the infinite q-deformed Heisenberg ferromagnet arXiv: Condensed Matter. ,(1995)
Nilanjana Datta, Tom Kennedy, Instability of interfaces in the antiferromagnetic XXZ chain at zero temperature Communications in Mathematical Physics. ,vol. 236, pp. 477- 511 ,(2003) , 10.1007/S00220-003-0826-4
Ky-Thuan Bach, Nicolas Macris, On kink states of ferromagnetic chains Physica A-statistical Mechanics and Its Applications. ,vol. 279, pp. 386- 397 ,(2000) , 10.1016/S0378-4371(99)00532-4
Francisco C. Alcaraz, S. R. Salinas, W. F. Wreszinski, Anisotropic ferromagnetic quantum domains. Physical Review Letters. ,vol. 75, pp. 930- 933 ,(1995) , 10.1103/PHYSREVLETT.75.930
Tohru Koma, Bruno Nachtergaele, Shannon Starr, The Spectral Gap for the Ferromagnetic Spin-J XXZ Chain Advances in Theoretical and Mathematical Physics. ,vol. 5, pp. 1047- 1090 ,(2001) , 10.4310/ATMP.2001.V5.N6.A3
TOHRU KOMA, BRUNO NACHTERGAELE, The Spectral Gap of the Ferromagnetic XXZ-Chain Letters in Mathematical Physics. ,vol. 40, pp. 1- 16 ,(1997) , 10.1023/A:1007351803403