RUS  ENG
Full version
JOURNALS // Symmetry, Integrability and Geometry: Methods and Applications

SIGMA, 2021, Volume 17, 112, 25 pp. (Mi sigma1794)

Form Factors of the Heisenberg Spin Chain in the Thermodynamic Limit: Dealing with Complex Bethe Roots
Nikolai Kitanine, Giridhar Kulkarni

References

1. Abada A., Bougourzi A. H., Si-Lakhal B., “Exact four-spinon dynamical correlation function of the Heisenberg model”, Nuclear Phys. B, 497 (1997), 733–753, arXiv: hep-th/9702028  crossref  mathscinet  zmath  adsnasa  scopus
2. Babelon O., de Vega H. J., Viallet C.-M., “Analysis of the Bethe ansatz equations of the $XXZ$ model”, Nuclear Phys. B, 220 (1983), 13–34  crossref  mathscinet  adsnasa  scopus
3. Babenko C., Göhmann F., Kozlowski K. K., Suzuki J., “A thermal form factor series for the longitudinal two-point function of the Heisenberg–Ising chain in the antiferromagnetic massive regime”, J. Math. Phys., 62 (2021), 041901, 49 pp., arXiv: 2011.12752  crossref  mathscinet  zmath  adsnasa  scopus
4. Bethe H., “Zur Theorie der Metalle. I. Eigenwerte und Eigenfunktionen der linearen Atomkette”, Z. Phys., 71 (1931), 205–226  crossref  adsnasa  scopus
5. Bougourzi A. H., Couture M., Kacir M., “Exact two-spinon dynamical correlation function of the one-dimensional Heisenberg model”, Phys. Rev. B, 54 (1996), R12669–R12672, arXiv: q-alg/9604019  crossref  adsnasa  scopus
6. Caux J.-S., Hagemans R., “The four-spinon dynamical structure factor of the Heisenberg chain”, J. Stat. Mech. Theory Exp., 2006 (2006), P12013, 14 pp., arXiv: cond-mat/0611319  crossref  scopus
7. Caux J.-S., Konno H., Sorrell M., Weston R., “Exact form-factor results for the longitudinal structure factor of the massless $XXZ$ model in zero field”, J. Stat. Mech. Theory Exp., 2012 (2012), P01007, 40 pp., arXiv: 1110.6641  crossref  mathscinet  scopus
8. Destri C., Lowenstein J. H., “Analysis of the Bethe-ansatz equations of the chiral-invariant Gross–Neveu model”, Nuclear Phys. B, 205 (1982), 369–385  crossref  mathscinet  adsnasa  scopus
9. Dugave M., Göhmann F., Kozlowski K. K., Suzuki J., “On form-factor expansions for the $XXZ$ chain in the massive regime”, J. Stat. Mech. Theory Exp., 2015 (2015), P05037, 49 pp., arXiv: 1412.8217  crossref  mathscinet  zmath  elib  scopus
10. Faddeev L. D., “Quantum completely integrable models in field theory”, Mathematical Physics Reviews, v. 1, Soviet Sci. Rev. Sect. C: Math. Phys. Rev., 1, Harwood Academic, Chur, 1980, 107–155  mathscinet
11. Faddeev L. D., Takhtajan L. A., “Spectrum and scattering of excitations in the one-dimensional isotropic Heisenberg model”, J. Sov. Math., 24 (1984), 241–267  mathnet  crossref  zmath  scopus
12. Faddeev L. D., Takhtajan L. A., What is the spin of a spin wave?, Phys. Lett. A, 85 (1981), 375–377  crossref  mathscinet  adsnasa  scopus
13. Foda O., Wheeler M., “Variations on Slavnov's scalar product”, J. High Energy Phys., 2012:10 (2012), 096, 23 pp., arXiv: 1207.6871  crossref  mathscinet  zmath  elib  scopus
14. Gaudin M., La fonction d'onde de Bethe, Collection du Commissariat à l'Énergie Atomique: Série Scientifique, Masson, Paris, 1983  mathscinet
15. Gaudin M., McCoy B. M., Wu T.T., “Normalization sum for the Bethe's hypothesis wave functions of the Heisenberg–Ising chain”, Phys. Rev. D, 23 (1981), 417–419  crossref  mathscinet  adsnasa  scopus
16. Jimbo M., Miki K., Miwa T., Nakayashiki A., “Correlation functions of the $XXZ$ model for $\Delta<-1$”, Phys. Lett. A, 168 (1992), 256–263, arXiv: hep-th/9205055  crossref  mathscinet  adsnasa  scopus
17. Jimbo M., Miwa T., Algebraic analysis of solvable lattice models, CBMS Regional Conference Series in Mathematics, 85, Amer. Math. Soc., Providence, RI, 1995  mathscinet  zmath
18. Jimbo M., Miwa T., Smirnov F., “Hidden Grassmann structure in the $XXZ$ model V: sine-Gordon model”, Lett. Math. Phys., 96 (2011), 325–365, arXiv: 1007.0556  crossref  mathscinet  zmath  adsnasa  elib  scopus
19. Kirillov A. N., Korepin V. E., “Norms of bound states”, J. Sov. Math., 40 (1988), 13–21  crossref  zmath  scopus
20. Kitanine N., Kozlowski K. K., Maillet J. M., Slavnov N. A., Terras V., “On the thermodynamic limit of form factors in the massless $XXZ$ Heisenberg chain”, J. Math. Phys., 50 (2009), 095209, 24 pp., arXiv: 0903.2916  crossref  mathscinet  zmath  adsnasa  elib  scopus
21. Kitanine N., Kozlowski K. K., Maillet J. M., Slavnov N. A., Terras V., “The thermodynamic limit of particle-hole form factors in the massless $XXZ$ Heisenberg chain”, J. Stat. Mech. Theory Exp., 2011 (2011), P05028, 34 pp., arXiv: 1003.4557  crossref  mathscinet  scopus
22. Kitanine N., Kozlowski K. K., Maillet J. M., Slavnov N. A., Terras V., “A form factor approach to the asymptotic behavior of correlation functions in critical models”, J. Stat. Mech. Theory Exp., 2011 (2011), P12010, 27 pp., arXiv: 1110.0803  crossref  mathscinet  scopus
23. Kitanine N., Kozlowski K. K., Maillet J. M., Slavnov N. A., Terras V., “Form factor approach to dynamical correlation functions in critical models”, J. Stat. Mech. Theory Exp., 2012 (2012), P09001, 33 pp., arXiv: 1206.2630  crossref  mathscinet  zmath  elib  scopus
24. Kitanine N., Kulkarni G., “Thermodynamic limit of the two-spinon form factors for the zero field $XXX$ chain”, SciPost Phys., 6 (2019), 076, 26 pp., arXiv: 1903.09058  crossref  mathscinet  adsnasa  scopus
25. Kitanine N., Maillet J. M., Terras V., “Form factors of the $XXZ$ Heisenberg spin-$\frac 12$ finite chain”, Nuclear Phys. B, 554 (1999), 647–678, arXiv: math-ph/9807020  crossref  mathscinet  zmath  adsnasa  scopus
26. Kitanine N., Maillet J. M., Terras V., “Correlation functions of the $XXZ$ Heisenberg spin-$\frac{1}{2}$ chain in a magnetic field”, Nuclear Phys. B, 567 (2000), 554–582, arXiv: math-ph/9907019  crossref  mathscinet  zmath  adsnasa  scopus
27. Korepin V. E., “Calculation of norms of Bethe wave functions”, Comm. Math. Phys., 86 (1982), 391–418  crossref  mathscinet  zmath  adsnasa  scopus
28. Kozlowski K. K., “Form factors of bound states in the $XXZ$ chain”, J. Phys. A: Math. Theor., 50 (2017), 184002, 83 pp., arXiv: 1611.01489  crossref  mathscinet  zmath  adsnasa  scopus
29. Kozlowski K. K., “Long-distance and large-time asymptotic behaviour of dynamic correlation functions in the massless regime of the $XXZ$ spin-1/2 chain”, J. Math. Phys., 60 (2019), 073303, 42 pp., arXiv: 1903.00207  crossref  mathscinet  zmath  adsnasa  scopus
30. Kulkarni G., Asymptotic analysis of the form-factors of quantum spin chains, Ph.D. Thesis, Université de Bourgogne, 2020
31. Maillet J. M., Terras V., “On the quantum inverse scattering problem”, Nuclear Phys. B, 575 (2000), 627–644, arXiv: hep-th/9911030  crossref  mathscinet  zmath  adsnasa  scopus
32. Mourigal M., Enderle M., Klöpperpieper A., Caux J.-S., Stunault A., Rønnow H. M., “Fractional spinon excitations in the quantum Heisenberg antiferromagnetic chain”, Nature Phys., 9 (2013), 435–441, arXiv: 1306.4678  crossref  adsnasa  elib  scopus
33. Sklyanin E. K., Takhtajan L. A., Faddeev L. D., “Quantum inverse problem method. I”, Theoret. and Math. Phys., 40 (1979), 688–706  mathnet  crossref  mathscinet  adsnasa  scopus
34. Slavnov N. A., “Calculation of scalar products of wave functions and form-factors in the framework of the algebraic Bethe ansatz”, Theoret. and Math. Phys., 79 (1989), 502–508  mathnet  crossref  mathscinet  adsnasa  scopus
35. Smirnov F. A., Form factors in completely integrable models of quantum field theory, Advanced Series in Mathematical Physics, 14, World Sci. Publ. Co., Inc., River Edge, NJ, 1992  crossref  mathscinet  zmath
36. Woynarovich F., “On the $S_z=0$ excited states of an anisotropic Heisenberg chain”, J. Phys. A: Math. Gen., 15 (1982), 2985–2996  crossref  mathscinet  adsnasa  scopus
37. Yang C. N., Yang C. P., “One-dimensional chain of anisotropic spin-spin interactions. I Proof of Bethe's hypothesis for ground state in a finite system”, Phys. Rev., 150 (1966), 321–327  crossref  mathscinet  adsnasa  scopus


© Steklov Math. Inst. of RAS, 2026