References[1] Heisenberg, W. 1928. Z. Phys., 49, 619.
[2] Bethe, H. 1931. Z. Phys., 71, 205.
[3] Hultén, L. 1938. Ark. Mat. Astron. Fys.B., 26A, 1.
[4] des Cloizeaux, J. and Pearson, J. J. 1962. Phys. Rev., 128, 2131.
[5] Yang, C. N. and Yang, C. P. 1966. Phys. Rev., 150, 321.
[6] Yang, C. N. and Yang, C. P. 1966. Phys. Rev., 150, 327.
[7] Baxter, R. J. 1971. Phys. Rev. Lett., 26, 832.
[8] Baxter, R. J. 1971. Phys. Rev. Lett., 26, 834.
[9] Baxter, R. J. 1972. Ann. Phys. (NY), 70, 193.
[10] Baxter, R. J. 1972. Ann. Phys. (NY), 70, 323.
[11] Johnson, J. D., Krinsky, S., and McCoy, B. M. 1973. Phys. Rev.A, 8, 2526.
[12] Sklyanin, E. K. and Faddeev, L. D. 1978. Dokl. Acad. Nauk SSSR, 243, 1430.
[13] Sklyanin, E. K. and Faddeev, L. D. 1978. Dokl. Acad. Nauk SSSR, 244, 1337.
[14] Gardner, C. S., Greene, J. M., Kruskal, M. D., and Miura, R. M. 1967. Phys. Rev. Lett., 19, 1095.
[15] Dubrovin, B. A., Matveev, V. B., and Novikov, S. P. 1976. Russian Math. Surveys, 31, 59.
[16] Takhtajan, L. A. and Faddeev, L. D. 1979. Russian Math. Surveys, 34, 11.
[17] Faddeev, L. D. and Takhtajan, L. A. 1984. J. Soviet. Math, 24, 241.
[18] Kulish, P. P., Reshetikhin, N. Yu., and Sklyanin, E. K. 1981. Lett. Math. Phys., 5, 393.
[19] Drinfel'd, V. G. 1985. Dokl. Acad. Nauk SSSR, 283, 1060.
[20] Jimbo, M. 1985. Lett. Math. Phys., 10, 63.
[21] Lieb, E. H. and Liniger, W. 1963. Phys. Rev., 130, 1605.
[22] Lieb, E. H. 1963. Phys. Rev., 130, 1616.
[23] Yang, C. N. and Yang, C. P. 1969. J. Math. Phys., 10, 1115.
[24] Sutherland, B. 1971. J. Math. Phys., 12, 246.
[25] Sutherland, B. 1971. J. Math. Phys., 12, 251.
[26] Yang, C. N. 1967. Phys. Rev. Lett., 19, 1312.
[27] Gaudin, M. 1967. Phys. Lett.A, 24, 55.
[28] Lai, C. K. 1971. Phys. Rev. Lett., 26, 1472.
[29] Lai, C. K. 1973. Phys. Rev.A, 8, 2567.
[30] Takahashi, M. 1971. Prog. Theor. Phys., 46, 1388.
[31] Takahashi, M. 1971. Prog. Theor. Phys., 46, 401.
[32] Gaudin, M. 1971. Phys. Rev. Lett., 26, 1301.
[33] Destri, C. and de Vega, H. J. 1992. Phys. Rev. Lett., 69, 2313.
[34] Destri, C. and De Vega, H. J. 1994. Nucl. Phys.B, 438, 413.
[35] Lieb, E. H. and Wu, F. Y. 1968. Phys. Rev. Lett., 20, 1445; Erratum: Phys. Rev. Lett., 21, 192.
[36] Andrei, N. 1980. Phys. Rev. Lett., 45, 379.
[37] Wiegmann, P. B. 1981. J. Phys.C, 14, 1463.
[38] Luttinger, J. M. 1963. J. Math. Phys., 4, 1154.
[39] Mattis, D. C. and Lieb, E. H. 1965. J. Math. Phys., 6, 304.
[40] Richardson, R. W., 1977. J. Math. Phys., 18, 1802.
[41] Coleman, S. 1975. Phys. Rev.D, 11, 2088.
[42] Karowski, M., Thun, H.-J., Truong, T. T., and Weisz, P. H. 1977. Phys. Lett.B, 67, 321.
[43] Zamolodchikov, A. B. and Zamolodchikov, Al. B. 1979. Ann. Phys. (N.Y.), 120, 253.
[44] Destri, C. and de Vega, H. J. 1991. Nucl. Phys.B, 358, 251.
[45] Zamolodchikov, Al. B. 1995. Int. J. Mod. Phys.A, 10, 1125.
[46] Onsager, L. 1944. Phys. Rev., 65, 117.
[47] Lieb, E. H. 1967. Phys. Rev. Lett., 18, 1046.
[48] Lieb, E. H. 1967. Phys. Rev. Lett., 19, 108.
[49] Lieb, E. H. 1967. Phys. Rev., 162, 162.
[50] Sutherland, B. 1967. Phys. Rev. Lett., 19, 103.
[51] Šamaj, L. and Travěnec, I. 2000. J. Stat. Phys., 101, 713.
[52] Kalinay, P. and Šamaj, L. 2002. J. Stat. Phys., 106, 857.
[53] Šamaj, L. 2003. J. Stat. Phys., 111, 261.
[54] Baxter, R. J. 1982. Exactly Solved Models in Statistical Mechanics. Academic Press.
[55] Gaudin, M. 1983. La Fonction d'Onde de Bethe. Masson.
[56] Mattis, D. C. 1993. The Many-Body Problem (An Encyclopedia of Exactly Solved Models in One Dimension). World Scientific.
[57] Korepin, V. E. and Essler, F. H. L. 1994. Exactly Solvable Models of Strongly Correlated Electrons. World Scientific.
[58] Gómez, C., Ruiz-Altaba, M., and Sierra, G. 1996. Quantum Groups in Two-Dimensional Physics. Cambridge University Press.
[59] Takahashi, M. 1999. Thermodynamics of One-dimensional Solvable Models. Cambridge University Press.
[60] Sutherland, B. 2004. Beautiful Models: 70 Years of Exactly Solved Quantum Many-Body Problems. World Scientific.
[61] Kuramoto, Y. and Kato, Y. 2009. Dynamics of One-Dimensional Quantum Systems (Inverse-Square Interaction Models). Cambridge University Press.
[62] Essler, F. H. L., Frahm, H., Göhmann, F., Klümper, A., and Korepin, V. E.2005. The One-Dimensional Hubbard Model. Cambridge University Press.
[63] Percus, J. K. and Šamaj, L. 1994. J. Stat. Phys., 77, 421.
[64] Jancovici, B. and Šamaj, L. 2001. J. Stat. Phys., 104, 753.
[65] Jancovici, B. and Šamaj, L. 2001. J. Stat. Phys., 105, 193.
[66] Jancovici, B. and Šamaj, L. 2005. Europhys. Lett., 72, 35.
[67] Jancovici, B. and Šamaj, L. 2009. Phys. Rev.E, 80, 031139.
[68] Šamaj, L. and Trizac, E. 2011. Phys. Rev. Lett., 106, 078301.
[69] Bajnok, Z., Palla, L., Takács, G., and Toth, G. Z. 2002. Nucl. Phys.B, 622, 548.
[70] Bajnok, Z., Rim, Ch., and Zamolodchikov, Al. 2008. Nucl. Phys.B, 796, 622.
[71] Bajnok, Z., Palla, L., and Takács, G. 2006. Nucl. Phys.B, 750, 179.
[72] Bajnok, Z. and El Deeb, O. 2010. Nucl. Phys.B, 832, 500.
[73] Bajnok, Z., Palla, L., and Takács, G. 2005. Nucl. Phys.B, 716, 519.
[74] Bajnok, Z. and Janik, R. A. 2009. Nucl. Phys.B, 807, 625.
[75] Šeba, P. 1986. Czech. J. Phys.B, 36, 667.
[76] Šeba, P. 1986. Rep. Math. Phys., 24, 111.
[77] De Vincenzo, S. and Sánchez, C. 2010, Can. J. Phys., 88, 809.
[78] Coutinho, F. A. B., Nogami, Y., and Perez, J. F. 1997. J. Phys. A: Math. Gen., 30, 3937.
[79] Cheon, T. and Shigehara, T. 1999. Phys. Rev. Lett., 82, 2536.
[80] Carreau, M. 1993. J. Phys. A: Math. Gen., 26, 427.
[81] Cheon, T. and Shigehara, T. 1998. Phys. Lett.A, 243, 111.
[82] Albeverio, S., Dabrowski, L., and Fei, S.-M. 2000. Int. J. Mod. Phys.B, 14, 721.
[83] McGuire, J. B. 1964. J. Math. Phys., 5, 622.
[84] Sneddon, L. N. 1966. Mixed Boundary Value Problem in Potential Theory. North-Holland.
[85] Hutson, V. 1963. Proc. Camb. Phil. Soc., 59, 211.
[86] Gaudin, M. 1971. Phys. Rev.A, 4, 386.
[87] Szegö, G. 1939. Orthogonal polynomials. Colloquium Publications Vol. 23. American Mathematical Society.
[88] Tonks, L. 1936. Phys. Rev., 50, 955.
[89] Wadati, M. and Kato, G. 2002. Chaos, Solitons & Fractals, 14, 23.
[90] Yang, C. P. 1970. Phys. Rev.A, 2, 154.
[91] Kato, G. and Wadati, M. 2001. Phys. Rev.E, 63, 036106.
[92] Kato, G. and Wadati, M. 2001. J. Phys. Soc. Jpn., 70, 1924.
[93] Birman, J. 1974. Ann. Math. Studies, 82, 1.
[94] Birman, J. 1983. Bull. Am. Math. Soc., 28, 253.
[95] Connes, A. 1994. Noncommutative Geometry. Academic Press.
[96] Wess, J. and Zumino, B. 1990. Nucl. Phys. B (Proc. Suppl.), 18, 302.
[97] McGuire, J. B. 1965. J. Math. Phys., 6, 432.
[98] McGuire, J. B. 1966. J. Math. Phys., 7, 123.
[99] Flicker, M. and Lieb, E. H. 1967. Phys. Rev., 161, 179.
[100] Sutherland, B. 1968. Phys. Rev. Lett., 20, 98.
[101] Takahashi, M. 1970. Prog. Theor. Phys., 44, 899.
[102] Lieb, E. H., Schultz, T. D., and Mattis, D. 1961. Ann. Phys. (N.Y.), 16, 407.
[103] Katsura, S. 1962. Phys. Rev., 127, 1508.
[104] Jordan, P. and Wigner, E. 1928. Z. Phys., 47, 631.
[105] Gradshteyn, I. S. and Ryzhik, I. M. 1994. Tables of Integrals, Series, and Products, 5th edn. Academic Press.
[106] Itzykson, C. and Drouffe, J.-M. 1989. Statistical Field Theory. Cambridge University Press.
[107] Sachdev, S. 1996. Nucl. Phys.B, 464, 576.
[108] Pfeuty, P. 1970. Ann. Phys. (N.Y.), 57, 79.
[109] Schultz, T. D., Mattis, D. C., and Lieb, E. H. 1964. Rev. Mod. Phys., 36, 856.
[110] Yang, C. N. and Yang, C. P. 1966. Phys. Rev., 151, 258.
[111] Orbach, R. 1958. Phys. Rev., 112, 309.
[112] Griffiths, R. B. 1964. Phys. Rev., 133A, 768.
[113] Bonner, C. and Fisher, M. E. 1964. Phys. Rev., 135A, 640.
[114] Krein, M. G. 1962. Am. Math. Soc. Trans.Ser. 2, 22, 163.
[115] Takahashi, M. and Suzuki, M. 1972. Prog. Theor. Phys., 48, 2187.
[116] Hida, K. 1981. Phys. Lett.A, 84, 338.
[117] Johnson, J. D. and McCoy, B. M. 1972. Phys. Rev.A, 6, 1613.
[118] Takahashi, M. 1973. Prog. Theor. Phys., 50, 1519.
[119] Blöte, H. W. J., Cardy, J. L., and Nightingale, M. P. 1986. Phys. Rev. Lett., 56, 742.
[120] Affleck, I. 1986. Phys. Rev. Lett., 56, 746.
[121] Vladimirov, A. A. 1984. Phys. Lett.A, 105, 418.
[122] Suzuki, J., Akutsu, Y., and Wadati, M. 1990. J. Phys. Soc. Jpn., 59, 2667.
[123] Klümper, A., Batchelor, M. T., and Pearce, P. A. 1991. J. Phys.A, 24, 3111.
[124] Klümper, A. 1992. Ann. Physik, 504, 540.
[125] Klümper, A. 1993. Z. Phys.B, 91, 507.
[126] Klümper, A. 2004. Lect. Notes Phys., 645, 349.
[127] Suzuki, M. 1985. Phys. Rev.B, 31, 2957.
[128] Suzuki, M. and Inoue, M. 1987. Prog. Theor. Phys., 78, 787.
[129] Baxter, R. J. 1973. Ann. Phys. (NY), 76, 1.
[130] Baxter, R. J. 1973. Ann. Phys. (NY), 76, 25.
[131] Baxter, R. J. 1973. Ann. Phys. (NY), 76, 48.
[132] Klümper, A. and Zittartz, J. 1989. Z. Phys.B, 75, 371.
[133] Suzuki, M. 1974. Prog. Theor. Phys., 51, 1992.
[134] Zamolodchikov, A. B. and Fateev, V. 1980. Yad. Fiz., 32, 581.
[135] Takhtajan, L. A. 1982. Phys. Lett.A, 87, 479.
[136] Babujian, H. M. 1982. Phys. Lett.A, 90, 479.
[137] Babujian, H. M. 1983. Nucl. Phys.B, 215, 317.
[138] Sogo, K. 1984. Phys. Lett.A, 104, 51.
[139] Takebe, T. 1992. J. Phys.A, 25, 1071.
[140] Takebe, T. 1996. J. Phys.A, 29, 6961.
[141] Sutherland, B. 1975. Phys. Rev.B, 12, 3795.
[142] Affleck, I., Kennedy, T., Lieb, E. H., and Tasaki, H. 1987. Phys. Rev. Lett., 59, 799.
[143] Affleck, I., Kennedy, T., Lieb, E. H., and Tasaki, H. 1988. Commun. Math. Phys., 115, 477.
[144] Takahashi, M. 1993. Phys. Rev.B, 48, 311.
[145] Haldane, F. D. M. 1983. Phys. Lett.A, 93, 464.
[146] Haldane, F. D. M. 1983. Phys. Rev. Lett., 50, 1153.
[147] Hubbard, J. 1963. Proc. R. Soc. (London)A, 276, 283.
[148] Mott, N. F. 1949. Proc. R. Soc. (London)A, 62, 416.
[149] Lieb, E. H. and Wu, F. Y. 2003. PhysicaA, 321, 1.
[150] Ovchinnikov, A. A. 1970. Sov. Phys. JETP, 30, 1160.
[151] Uimin, G. V. and Fomichev, S. V. 1973. Sov. Phys. JETP, 36, 1001.
[152] Woynarovich, F. 1982. J. Phys.C, 15, 85.
[153] Woynarovich, F. 1982. J. Phys.C, 15, 97.
[154] Woynarovich, F. 1983. J. Phys.C, 16, 5293.
[155] Schadschneider, A. and Zittartz, J. 1991. Z. Phys.B, 82, 387.
[156] Takahashi, M. 1969. Prog. Theor. Phys., 42, 1098.
[157] Takahashi, M. 1970. Prog. Theor. Phys., 43, 1619.
[158] Takahashi, M. 1970. Prog. Theor. Phys., 43, 860.
[159] Shiba, H. 1972. Phys. Rev.B, 6, 930.
[160] Woynarovich, F. and Bahder, T. B. 1986. Phys. Rev.B, 33, 2114.
[161] Woynarovich, F. 1983. J. Phys.C, 16, 6593.
[162] Takahashi, M. 1972. Prog. Theor. Phys., 47, 69.
[163] Takahashi, M. 1974. Prog. Theor. Phys., 52, 103.
[164] Deguchi, T. et al. 2000. Phys. Rep., 331, 197.
[165] Essler, F., Korepin, V., and Schoutens, K. 1992. Nucl. Phys.B, 384, 431.
[166] Koma, T. 1987. Prog. Theor. Phys., 78, 1213.
[167] Koma, T. 1989. Prog. Theor. Phys., 81, 783.
[168] Klümper, A. and Bariev, R. Z. 1996. Nucl. Phys.B, 458, 623.
[169] Jüttner, G., Klümper, A., and Suzuki, J. 1998. Nucl. Phys.B, 522, 471.
[170] Kondo, J. 1964. Prog. Theor. Phys., 32, 37.
[171] Andrei, N., Furuya, K., and Lowenstein, J. H. 1983. Rev. Mod. Phys., 55, 331.
[172] Tsvelick, A. M. and Wiegmann, P. B.Adv. Phys., 32, 453.
[173] Vousovskii, S. 1946. JETP, 16, 981.
[174] Zener, C. 1951. Phys. Rev., 81, 440.
[175] Anderson, P. W. 1961. Phys. Rev., 124, 41.
[176] Anderson, P. W. 1978. Rev. Mod. Phys., 50, 191.
[177] Fateev, V. A. and Wiegmann, P. B. 1981. Phys. Lett.A, 81, 179.
[178] Furuya, K. and Lowenstein, J. M. 1982. Phys. Rev.B, 25, 5935.
[179] Abrikosov, A. A. and Migdal, A. A. 1970. J. Low Temp. Phys., 3, 519.
[180] Fowler, M. and Zawadowski, A. 1971. Solid State Commun., 9, 471.
[181] Filyov, V. M., Tsvelick, A. M., and Wiegmann, P. B. 1981. Phys. Lett.A, 81, 115.
[182] Fateev, V. A. and Wiegmann, P. B. 1981. Phys. Rev. Lett., 46, 1595.
[183] Pines, D. and Nozières, P. 1966. The Theory of Quantum Liquids. Addison-Wesley.
[184] Schultz, H. J., Cuniberti, G., and Pieri, P. 1998. arXiv:cond-mat/9807366.
[185] Tomonaga, S. 1950. Prog. Theor. Phys., 5, 544.
[186] Luther, A. and Peschel, I. 1974. Phys. Rev.B, 9, 2911.
[187] Haldane, F. D. M. 1981. J. Phys.C, 14, 2585.
[188] Giuliani, G. F. and Vignale, G. 2005. Quantum Theory of the Electron Liquid. Cambridge University Press.
[189] Gogolin, A. O., Nersesyan, A. A., and Tsvelik, A. M. 1998. Bosonization and Strongly Correlated Systems. Cambridge University Press.
[190] Bardeen, J., Cooper, L. N., and Schrieffer, J. R. 1957. Phys. Rev., 108, 1175.
[191] Bogoliubov, N. N., Tolmachev, V. V., and Shirkov, D. V. 1959. A New Method in the Theory of Superconductivity. Consultants Bureau, New York.
[192] von Delft, J. and Poghossian, R., 2002. Phys. Rev.B, 66, 134502.
[193] Gaudin, M., 1968. États propres et valeurs propres de l'Hamiltonian d'appariement, unpublished Saclay preprint.
[194] Fröhlich, H., 1950. Phys. Rev., 79, 845.
[195] Cambiaggio, M. C., Rivas, A. M. F., and Saraceno, M., 1997. Nucl.Phys.A, 624, 157.
[196] Gaudin, M., 1976. J. Phys., 37, 1087.
[197] Hogaasen-Feldman, J., 1961. Nucl.Phys., 28, 258.
[198] Sierra, G., Dukelsky, J., Dussel, G. G., von Delft, J., and Braun, F., 2000. Phys. Rev.B, 61, 11890.
[199] Asorey, M., Falceto, F., and Sierra, G., 2002. Nucl. Phys.B, 622, 593.
[200] Richardson, R. W., 1968. J. Math. Phys., 9, 1327.
[201] Dukelsky, J. and Schuck, P., 2001. Phys. Rev. Lett., 86, 4207.
[202] Rajaraman, R. 1982 Solitons and Instantons. An Introduction to Solitons and Instantons in Quantum Field theory. North-Holland, p. 409.
[203] Rogers, C. and Shadwick, W. F. 1982. Bäcklund Transformations and their Applications. Academic Press, p. 334.
[204] Hirota, R. 1992. Direct Methods in Soliton Theory. Cambridge University Press.
[205] Ablowitz, M. J., Kaup, D. J., Newell, A. C., and Segur, Y. 1973. Phys. Rev. Lett., 31, 125.
[206] Faddeev, L. D. and Takhtajan, L. A. 1974. Teor. Mat. Fiz., 21, 160.
[207] Fring, A., Mussardo, G., and Simonetti, P. 1993. Nucl. Phys. B393 413.
[208] Ginsparg, P. H. 1988. Applied Conformal Field Theory. Les Houches Summer School, pp. 1–168.
[209] Di Francesco, P., Mathieu, P., and Senechal, D. 1997. Conformal Field Theory. Springer.
[210] Yurov, V. P. and Zamolodchikov, A. B. 1989. Int. J. Mod. Phys.A, 5, 3221.
[211] Feverati, G., Ravanini, F., and Takács, G. 1998 Nucl. Phys.B, 540 543.
[212] Zamolodchikov, A. B. 1989. Adv. Stud. Pure Math., 19 641.
[213] Mussardo, G. 1992. Phys. Rep., 218, 215.
[214] Jackiw, R. and Woo, G. 1975. Phys. Rev.D, 12 1643.
[215] Itzykson, C. and Zuber, J. B. 1980. Quantum Field Theory. McGraw-Hill.
[216] Vergeles, S. N. and Gryanik, V. M. 1976. Yad. Fiz., 23 1324.
[217] Schroer, B., Truong, T. T., and Weisz, P. H. 1976. Phys. Lett.B, 63 422.
[218] Coleman, S. R. and Norton, R. E. 1965. Nuovo Cim., 38, 438.
[219] Coleman, S. R. and Thun, H. J. 1978. Commun. Math. Phys., 61, 31.
[220] Dorey, P. 1996. Exact S matrices, in the Proceedings of the 1996 Eötvös Graduate School. Springer, pp 85–125.
[221] Arefeva, I. and Korepin, V. 1974. Pisma Zh. Eksp. Teor. Fiz., 20, 680.
[222] Cardy, J. L. and Mussardo, G. 1989. Phys. Lett.B, 225, 275.
[223] Smirnov, F. A. 1989. Int. J. Mod. Phys.A, 4 4213.
[224] Fioravanti, D. and Rossi, M. 2005. JHEP, 08:010.
[225] Fioravanti, D., Mariottini, A., Quattrini, E., and Ravanini, F. 1997. Phys. Lett.B, 390 243.
[226] Feverati, G., Ravanini, F., and Takács, G. 1998. Phys. Lett.B, 430, 264.
[227] Feverati, G., Ravanini, F., and Takács, G. 1998. Phys. Lett.B, 444, 442.
[228] Feverati, G., Ravanini, F., and Takács, G. 2000. Nucl. Phys.B, 570, 615.
[229] Martin, Ph. A. 1988. Rev. Mod. Phys., 60, 1075.
[230] Lieb, E. H. and Lebowitz, J. L. 1972. Adv. Math., 9, 316.
[231] Kosterlitz, J. M. and Thouless, D. J. 1973. J. Phys.C, 6, 1181.
[232] Hansen, J. P. and Viot, P. 1985. J. Stat. Phys., 38, 823.
[233] Hansen, J. P. and McDonald, I. R. 2006. Theory of Simple Liquids, 3rd edn. Academic Press.
[234] Deutsch, C. and Lavaud, M. 1974. Phys. Rev.A, 9, 2598.
[235] Kalinay, P., Markoš, P., Šamaj, L., and Travěnec, I. 2000. J. Stat. Phys., 98, 639.
[236] Jancovici, B., Kalinay, P., and Šamaj, L. 2000. PhysicaA, 279, 260.
[237] Edwards, S. F. 1959. Philos. Mag., 4, 1171.
[238] Brydges, D. and Federbush, P. 1980. Commun. Math. Phys., 73, 197.
[239] Minnhagen, P. 1987. Rev. Mod. Phys., 59, 1001.
[240] Hauge, E. H. and Hemmer, P. C. 1971. Phys. Norvegica, 5, 209.
[241] Dodd, R. K. and Bullough, R. K. 1977. Proc. R. Soc. (London)A, 352, 481.
[242] Fateev, V. A., Zamolodchikov, A. B., and Zamolodchikov, Al. B. 1998. Nucl. Phys.B, 516, 652.
[243] Jacobi, K. G. 1829. Fundamenta Nova Theoriae Functionum Ellipticarum. Königsberg.
[244] Whittaker, E. T. and Watson, G. N. 1927. A Course of Modern Analysis, 4th edn. Cambridge University Press.