  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 multiple
integral formula for the general correlations is derived. But the integration
of this formula is also very difficult problem. Recently these integrals are
decomposed to products of one dimensional integrals and at zero temperature,
zero magnetic field and isotropic case, correlation functions are expressed by
$\log 2$ and Riemann's zeta functions with odd integer argument
$\zeta(3),\zeta(5),\zeta(7),...$. We can calculate density sub-matrix of
successive seven sites. Entanglement entropy of seven sites is calculated.
These methods can be extended to XXZ chain up to $n=4$. Correlation functions
are expressed by the generalized zeta functions. Several years ago I derived
new thermodynamic Bethe ansatz equation for XXZ chain. This is quite different
with Yang-Yang type TBA equations and contains only one unknown function. This
equation is very useful to get the high temperature expansion. In this paper we
get the analytic solution of this equation at $\Delta=0$.
