Geodesic
Asymptotic expansions for correlation functions of one-dimensional bosons
Teoretičeskaâ i matematičeskaâ fizika, Tome 174 (2013) no. 1, pp. 125-139 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We discuss different asymptotic representations for correlation functions of critical integrable systems. We prove that in the one-dimensional boson model, the asymptotic series for correlation functions obtained by the multiple-integral method coincides with the conformal field theory predictions in the low-temperature limit.
Keywords: correlation function, asymptotic expansion. 
@article{TMF_2013_174_1_a8,
     author = {N. A. Slavnov},
     title = {Asymptotic expansions for correlation functions of one-dimensional bosons},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {125--139},
     year = {2013},
     volume = {174},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2013_174_1_a8/}
}
TY  - JOUR
AU  - N. A. Slavnov
TI  - Asymptotic expansions for correlation functions of one-dimensional bosons
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2013
SP  - 125
EP  - 139
VL  - 174
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_2013_174_1_a8/
LA  - ru
ID  - TMF_2013_174_1_a8
ER  - 
%0 Journal Article
%A N. A. Slavnov
%T Asymptotic expansions for correlation functions of one-dimensional bosons
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2013
%P 125-139
%V 174
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_2013_174_1_a8/
%G ru
%F TMF_2013_174_1_a8
N. A. Slavnov. Asymptotic expansions for correlation functions of one-dimensional bosons. Teoretičeskaâ i matematičeskaâ fizika, Tome 174 (2013) no. 1, pp. 125-139. http://geodesic.mathdoc.fr/item/TMF_2013_174_1_a8/

[1] K. K. Kozlowski, J. M. Maillet, N. A. Slavnov, J. Stat. Mech., 3 (2011), P03018, 38 pp. | DOI

[2] K. K. Kozlowski, J. M. Maillet, N. A. Slavnov, J. Stat. Mech., 3 (2011), P03019, 25 pp. | DOI

[3] N. Kitanine, K. K. Kozlowski, J. M. Maillet, N. A. Slavnov, V. Terras, J. Stat. Mech., 12 (2011), P12010, 28 pp., arXiv: 1110.0803 | DOI

[4] A. A. Belavin, A. M. Polyakov, A. B. Zamolodchikov, Nucl. Phys. B, 241:2 (1984), 333–380 | DOI | MR | Zbl

[5] J. L. Cardy, J. Phys. A, 17:7 (1984), L385–L387 | DOI | MR

[6] J. L. Cardy, Nucl. Phys. B, 270:2 (1986), 186–204 | DOI | MR | Zbl

[7] H. Bethe, Z. Phys., 71:3–4 (1931), 205–226 | DOI

[8] R. Orbach, Phys. Rev., 112:2 (1958), 309–316 | DOI

[9] E. H. Lieb, W. Liniger, Phys. Rev., 130:4 (1963), 1605–1616 | DOI | MR | Zbl

[10] E. H. Lieb, D. C. Mattis, Mathematical Physics in One Dimension, Acad. Press, New York, 1966

[11] H. J. de Vega, F. Woynarovich, Nucl. Phys. B, 251:3 (1985), 439–456 | DOI | MR

[12] H. W. Blöte, J. L. Cardy, M. P. Nightingale, Phys. Rev. Lett., 56:7 (1986), 742–745 | DOI

[13] I. Affleck, Phys. Rev. Lett., 56:7 (1986), 745–748 | DOI | MR

[14] N. Bogolyubov, A. Izergin, N. Reshetikhin, Pisma v ZhETF, 44:9 (1986), 405–407 | MR

[15] A. Berkovich, G. Murthy, J. Phys. A, 21:7 (1988), L395–L400 | DOI | MR | Zbl

[16] A. Berkovich, G. Murthy, J. Phys. A, 21:19 (1988), 3703–3721 | DOI | MR | Zbl

[17] A. Klümper, M. Batchelor, J. Phys. A, 23:5 (1990), L189–L195 | DOI | MR | Zbl

[18] A. Klümper, M. Batchelor, P. Pearce, J. Phys. A, 24:13 (1991), 3111–3133 | DOI | MR | Zbl

[19] A. Klümper, Z. Phys. B, 91:4 (1993), 507–519, arXiv: cond-mat/9306019 | DOI | MR

[20] A. Klümper, T. Wehner, J. Zittartz, J. Phys. A, 26:12 (1993), 2815–2827 | DOI | MR | Zbl

[21] A. Klümper, “Integrability of quantum chains: Theory and applications to the spin-1/2 $XXZ$ chain”, Quantum Magnetism, Lecture Notes in Physics, 645, eds. U. Schollwock, J. Richter, D. J. J. Farnell, R. F. Bishop, Springer, Berlin, 2004, 349–379, arXiv: cond-mat/0502431 | DOI

[22] A. Seel, T. Bhattacharyya, F. Göhmann, A. Klümper, J. Stat. Mech., 8 (2007), P08030, 11 pp. | DOI | MR

[23] C. N. Yang, C. P. Yang, J. Math. Phys., 10:7 (1969), 1115–1122 | DOI | MR | Zbl

[24] C. P. Yang, Phys. Rev. A, 2:1 (1970), 154–157 | DOI

[25] M. Takahashi, Prog. Theor. Phys., 46:2 (1971), 401–415 | DOI | MR

[26] M. Gaudin, Phys. Rev. Lett., 26:21 (1971), 1301–1304 | DOI

[27] E. K. Sklyanin, L. A. Takhtadzhyan, L. D. Faddeev, TMF, 40:2 (1979), 194–220 | DOI | MR

[28] L. D. Faddeev, “How algebraic Bethe ansatz works for integrable models”, Symétries quantiques (Les Houches, August 1 – September 8, 1995), eds. A. Connes, K. Gawedzki, J. Zinn-Justin, North-Holland, Amsterdam, 1998, 149–219 | MR | Zbl

[29] V. E. Korepin, N. M. Bogoliubov, A. G. Izergin, Quantum Inverse Scattering Method and Correlation Functions, Cambridge Univ. Press, Cambridge, 1993 | MR | Zbl

[30] N. M. Bogolyubov, V. E. Korepin, TMF, 60:2 (1984), 262–269 | DOI | MR

[31] N. M. Bogoliubov, A. G. Izergin, V. E. Korepin, “Quantum inverse scattering method and correlation functions”, Exactly Solvable Problems in Condensed Matter and Relativistic Field Theory, Proceedings of the Winter School and International Colloquium (Panchgani, January 30 – February 12, 1985), Lecture Notes in Physics, 242, eds. B. S. Shastry, S. S. Jha, V. Singh, Springer, Berlin, 1985, 220–316 | DOI | MR

[32] J. D. Johnson, B. M. McCoy, Phys. Rev. A, 6:4 (1972), 1613–1626 | DOI

[33] L. Mezincescu, R. I. Nepomechie, “Introduction to the thermodynamics of spin chains”, Quantum Groups, Integrable Models and Statistical Systems (Kingston, Canada, 13–17 July, 1992), eds. J. LeTourneux, L. Vinet, World Scientific, Singapore, 1993, 168–191, arXiv: hep-th/9212124

[34] N. A. Slavnov, TMF, 121:1 (1999), 117–138 | DOI | MR | Zbl

[35] S. V. Kerov, Funkts. analiz i ego pril., 34:1 (2000), 51–64 | DOI | MR | Zbl

[36] A. Borodin, G. Olshanski, Electron. J. Combin., 7 (2000), R28, 39 pp. | MR | Zbl

[37] A. Borodin, G. Olshanski, Commun. Math. Phys., 211:2 (2000), 335–358, arXiv: math/9904010 | DOI | MR | Zbl

[38] A. Okounkov, “$SL(2)$ and $z$-measures”, Random Matrix Models and Their Applications, Mathematical Sciences Research Institute Publications, 40, eds. P. Bleher, A. Its, Cambridge Univ. Press, Cambridge, 2001, 407–420 | MR | Zbl

[39] N. Kitanine, K. K. Kozlowski, J. M. Maillet, N. A. Slavnov, V. Terras, J. Stat. Mech., 5 (2011), P05028, 34 pp. | DOI

[40] N. Kitanine, K. K. Kozlowski, J. M. Maillet, N. A. Slavnov, V. Terras, J. Math. Phys., 50:9 (2009), 095209, 24 pp., arXiv: 0903.2916 | DOI | MR | Zbl

[41] N. Kitanine, K. K. Kozlowski, J. M. Maillet, N. A. Slavnov, V. Terras, J. Stat. Mech., 1 (2007), P01022, 17 pp. | DOI | MR