The spectral gap for the ferromagnetic spin-J XXZ chain

Advances in Theoretical and Mathematical Physics

Volumn 5, Issue 6, 2001, Pages 1047-1090

  Koma, Tohru ^a   Nachtergaele, Bruno ^b   Starr, Shannon ^c  

^a GAKUSHUIN UNIVERSITY   (Japan)

^b UNIVERSITY OF CALIFORNIA   (United States)

^c PRINCETON UNIVERSITY   (United States)

Author keywords

Anisotropic heisenberg ferromagnet; XXZ model

Indexed keywords

EID: 79551491182     PISSN: 10950761     EISSN: 10950753     Source Type: Journal    
DOI: 10.4310/atmp.2001.v5.n6.a3     Document Type: Article

References (29)

1. F. C. Alcaraz, S. R. Salinas, and W. F. Wreszinski, Anisotropic ferromagnetic quantum domains, Phys. Rev. Lett 75 (1995), 930-933.
2. George Andrews, The theory of partitions, Encyclopedia of Mathematics and its Applications, vol. 2, Addison Wesley, Reading, MA, 1976.
3. O. Bolina, P. Contucci, and B. Nachtergaele, Path integral representation for interface states of the anisotropic Heisenberg model, Rev. Math. Phys. 12 (2000), no. 10, 1325-1344.
4. O. Bolina, P. Contucci, B. Nachtergaele, and S. Starr, A continuum approximation for the excitations of the (1,1,...,1) interface in the quantum heisenberg model, Electron. J. Diff. Eqns. (2000), 1-10.
5. O. Bolina, P. Contucci, B. Nachtergaele, and S. Starr,, Finite-volume excitations of the 111 interface in the quantum XXZ model, Comm. Math. Phys. 212 (2000), 63-91.
6. P. Caputo and F. Martinelli, Asymmetric diffusion and the energy gap above the 111 ground state of the quantum xxz model, Commun. Math. Phys. 226 (2002), no. 2, 323-375.
7. P. Caputo and F. Martinelli, Relaxation time of anisotropic simple exclusion processes and quantum heisenberg models, preprint, 2002.
8. Joseph Conlon and Jan Philip Solovej, On asymptotic limits for the quantum heisenberg model, J. Phys. A: Math. Gen. 23 (1990), 3199-3213.
9. Freeman Dyson, General theory of spin-wave interactions, Phys. Rev. 102 (1956), no. 5, 1217-1230.
10. Freeman Dyson, Thermodynamic behavior of an ideal ferromagnet, Phys. Rev. 102 (1956), no. 5, 1230-1244.
11. G. Gasper and M. Rahman, Basic hypergeometric series, Encyclopedia of Mathematics and Its Applications, vol. 35, Cambridge University Press, Cambridge, England, 1990.
12. C.-T. Gottstein and R. F. Werner, Ground states of the infinite q-deformed Heisenberg ferromagnet, Preprint.
13. T. Holstein and H. Primakoff, Field dependence of the intrinsic domain ma-gentization of a ferromagnet, Phys. Rev. 58 (1940), 1098-1113.
14. M. Jimbo and T. Miwa, Algebraic analysis of solvable lattice models, Regional Conference Series in Mathematics, American Mathematical Society, Providence, RI, 1995.
15. C. Kassel, Quantum groups, Springer Verlag, New York, NY, 1995.
16. T. Koma and B. Nachtergaele, The spectral gap of the ferromagnetic XXZ chain, Lett. Math. Phys. 40 (1997), 1-16.
17. T. Koma and B. Nachtergaele, The complete set of ground states of the ferromagnetic XXZ chains, Adv. Theor. Math. Phys. 2 (1998), 533-558.
18. T. Koma and Masanori Yamanaka, Resistance jumps and hysteresis in ferromagnetic wires, Phys. Rev. B 65 (2002), in press.
19. E. Lieb, The classical limit of quantum spin systems, Commun. Math. Phys. 31 (1973), 681-683.
20. E. Lieb and D. Mattis, Theory of ferromagnetism and the ordering of electronic energy levels, Phys. Rev. 125 (1962), 164-172.
21. T. Matsui, On ground states of the one-dimensional ferromagnetic XXZ model, Lett. Math. Phys. 37 (1996), 397.
22. A. Messager and B. Nachtergaele, Interface states of quantum spin systems, Mathematical Results in Statistical Mechanics (S. Miracle-Soĺe, ed.), World Scientific, Singapore, 1999, pp. 287-299.
23. T. Michoel and A. Verbeure, Mathematical structure of magnons in quantum ferromagnets, J. Phys. A: Math. Gen. 32 (1999), 5875-5883.
24. B. Nachtergaele and S. Starr, in preparation.
25. B. Nachtergaele and S. Starr, Droplet states in the XXZ Heisenberg model, Comm. Math. Phys. 218 (2001), 569-607.
26. V. Pasquier and H. Saleur, Common structures between finite systems and con-formal field theories through quantum groups, Nuclear Physics B 330 (1990), 523-556.
27. R. P. Stanley, Enumerative combinatorics, vol. 2, Cambridge University Press, Cambridge, UK, 1999.
28. Shannon Starr, Some properties of the low lying spectrum of the quantum xxz spin system, Ph.D. thesis, U. C. Davis, Davis, CA 95616, June 2001.
29. M. Yamanaka and T. Koma, Scattering of conduction electrons by a ferromagnetic domain wall, J. Magn. Soc. Japan 23 (1999), 141-143.