Correlation function and simplified TBA equations for XXZ chain

Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

Volumn 7, Issue , 2011, Pages

  Takahashi, Minoru ^a  

^a UNIVERSITY OF WUPPERTAL   (Germany)

Author keywords

Correlation function; Thermodynamic bethe ansatz equation

Indexed keywords

EID: 84896061787     PISSN: None     EISSN: 18150659     Source Type: Journal    
DOI: 10.3842/SIGMA.2011.004     Document Type: Article

References (36)

1. Takahashi M., Half-filled Hubbard model at low temperature, J. Phys. C 10 (1977), 1289-1301.
2. Yang C.N., Yang C.P., Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction, J. Math. Phys. 10 (1969), 1115-1122.
3. Takahashi M., One-dimensional Heisenberg model at finite temperature, Prog. Theor. Phys. 46 (1971), 401-415.
4. Gaudin M., Thermodynamics of the Heisenberg-Ising ring for 1, Phys. Rev. Lett. 26 (1971), 1301-1304.
5. Takahashi M., Suzuki M., One-dimensional anisotropic Heisenberg model at finite temperatures, Prog. Theor. Phys. 46 (1972), 2187-2209.
6. Koma T., Thermal Bethe-ansatz method for the spin-1/2 XXZ Heisenberg chain, Prog. Theor. Phys. 81 (1989), 783-809.
7. Takahashi M., Correlation length and free energy of S = 1=2 XXZ chain in magnetic field, Phys. Rev. B 44 (1991), 12382-12394.
8. Klümper A., Thermodynamics of the anisotropic spin-1/2 Heisenberg chain and related quantum chains, Z. Phys. B 91 (1993), 507-519, cond-mat/9306019.
9. Takahashi M., Simplification of thermodynamic Bethe-ansatz equations, in Physics and Combinatrix (Nagoya, 2000), World Sci. Publ., River Edge, NJ, 2001, 299-304, cond-mat/0010486.
10. Takahashi M., Shiroishi M., Klumper A., Equivalence of TBA and QTM, J. Phys. A: Math. Gen. 34 (2001), L187-L194, cond-mat/0102027.
11. Shiroishi M., Takahashi M., Integral equation generates high-temperature expansion of the Heisenberg chain, Phys. Rev. Lett. 89 (2002), 117201, 4 pages, cond-mat/0205180.
12. Tsuboi Z., Takahashi M., Nonlinear integral equations for thermodynamics of the Uq(sl\(r + 1)) Perk-Schultz model, J. Phys. Soc. Japan 74 (2005), 898-904, cond-mat/0412698.
13. Hulth-en L., Über das Austauschproblem eines Kristalles, Ark. Mat. Astron. Fys. A 26 (1938), 1-105.
14. Muramoto N., Takahashi M., Integrable magnetic model of two chains coupled by four-body interactions, J. Phys. Soc. Japan 68 (1999), 2098-2104, cond-mat/9902007.
15. Jimbo M., Miki K., Miwa T., Nakayashiki A., Correlation functions of the XXZ model for Δ < -1, Phys. Lett. A 168 (1992), 256-263, hep-th/9205055.
16. Nakayashiki A., Some integral formulas for the solutions of the sl2 dKZ equation with level-4, Internat. J. Modern Phys. A 9 (1994), 5673-5687.
17. Jimbo M., Miwa T., Quantum KZ equation with jqj = 1 and correlation functions of the XXZ model in the gapless regime, J. Phys. A: Math. Gen. 29 (1996), 2923-2958, hep-th/9601135.
18. Kitanine N., Maillet J.M., Terras V., Correlation functions of the XXZ Heisenberg spin-1/2 chain in a magnetic field, Nuclear Phys. B 567 (2000), 554-582, math-ph/9907019
19. Göhmann F., Klüumper A., Seel A., Integral representations for correlation functions of the XXZ chain at finite temperature, J. Phys. A: Math. Gen. 37 (2004), 7625-7651, hep-th/0405089.
20. Boos H.E., Korepin V.E., Quantum spin chains and Riemann zeta function with odd arguments, J. Phys. A: Math. Gen. 34 (2001), 5311-5316, hep-th/0104008.
21. Boos H.E., Korepin V.E., Evaluation of integrals representing correlations in XXX Heisenberg spin chain, in MathPhys Odyssey (2001), Prog. Math. Phys., Vol. 23, Birkhäuser Boston, Boston, MA, 2002, 65-108, hep-th/0105144.
22. Sakai K., Shiroishi M., Nishiyama Y., Takahashi M., Third-neighbor correlators of a one-dimensional spin- 1/2 Heisenberg antiferromagnet, Phys. Rev. E 67 (2003), 065101(R), 4 pages, cond-mat/0302564.
23. Boos H.E., Korepin V.E., Nishiyama Y., Shiroishi M., Quantum correlations and number theory, J. Phys. A: Math. Gen. 35 (2002), 4443-4451, cond-mat/0202346.
24. Boos H.E., Korepin V.E., Smirnov F.A., Emptiness formation probability and quantum Knizhnik- Zamolodchikov equation, Nuclear Phys. B 658 (2003), 417-439, hep-th/0209246.
25. Boos H.E., Shiroishi M., Takahashi M., First principle approach to correlation functions of spin-1/2 Heisenberg chain: fourth-neighbor correlators, Nuclear Phys. B 712 (2005), 573-599, hep-th/0410039.
26. Sato J., Shiroishi M., Takahashi M., Correlation functions of the spin-1/2 anti-ferromagnetic Heisenberg chain: exact calculation via the generating function, Nuclear Phys. B 729 (2005), 441-466, hep-th/0507290.
27. Boos H., Jimbo M., Miwa T., Smirnov F., Takeyama Y., A recursion formula for the correlation functions of an inhomogeneous XXX model, St. Petersburg Math. J. 17 (2005), 85-117, hep-th/0405044.
28. Boos H., Jimbo M., Miwa T., Smirnov F., Takeyama Y., Reduced qKZ equation and correlation functions of the XXZ model, Comm. Math. Phys. 261 (2006), 245-276, hep-th/0412191.
29. Boos H., Jimbo M., Miwa T., Smirnov F., Takeyama Y., Traces on the Sklyanin algebra and correlation functions of the eight-vertex model, J. Phys. A: Math. Gen. 38 (2005), 7629-7659, hep-th/0504072.
30. Boos H., Jimbo M., Miwa T., Smirnov F., Takeyama Y., Density matrix of a finite sub-chain of the Heisenberg anti-ferromagnet, Lett. Math. Phys. 75 (2006), 201-208, hep-th/0506171.
31. Kato G., Shiroishi M., Takahashi M., Sakai K., Next nearest-neighbor correlation functions of the spin-1/2 XXZ chain at critical region, J. Phys. A: Math. Gen. 36 (2003), L337-L344, cond-mat/0304475.
32. Takahashi M., Kato G., Shiroishi M., Next nearest-neighbor correlation functions of the spin-1/2 XXZ chain at massive region, J. Phys. Soc. Japan 73 (2004), 245-253, cond-mat/0308589.
33. Kato G., Shiroishi M., Takahashi M., Sakai K., Third-neighbour and other four-point correlation functions of spin-1/2 XXZ chain, J. Phys. A: Math. Gen. 37 (2004), 5097-5123, cond-mat/0402625.
34. Takahashi M., Thermodynamics of one-dimensional solvable models, Cambridge University Press, Cambridge, 1999.
35. Lieb E.H., Wu F.Y., Absence of mott transition in an exact solution of the short-range, one-band model in one dimension, Phys. Rev. Lett. 20 (1968), 1445-1448, Erratum, Phys. Rev. Lett. 21 (1968), 192.
36. Takahashi M., On the exact ground state energy of Lieb and Wu, Prog. Theor. Phys. 45 (1971), 756-760.