| The calculation of the correlation functions of Bethe ansatz solvable models is very difficult problem. Among these solvable models spin 1/2 XXX chain has been investigated for a long time. Even for this model only the nearest neighbor and the second neighbor correlations were known. In 1990's Kyoto group gave multiple integral formula for the general correlations. But the integration of this formula is also very difficult problem. Recently these integrals are decomposed to products of one dimensional integrals and correlation functions are expressed by log(2) and Riemann's zeta functions with odd integer argument ζ(3), ζ(5), ζ(7),.... We can calculate density matrix of successive six sites. This means that all correlations in successive 6 sites can be calculated. These method can be extended to XXZ chain. I will review recent progress in the calculations of correlation functions. |
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