  We derive a multiple integral representing the ground state density matrix of
a segment of length $m$ of the XXZ spin chain on $L$ lattice sites, which
depends on $L$ only parametrically. This allows us to treat chains of arbitrary
finite length. Specializing to the isotropic limit of the XXX chain we show for
small $m$ that the multiple integrals factorize. We conjecture that this
property holds for arbitrary $m$ and suggest an exponential formula for the
density matrix which involves only a double Cauchy type integral in the
exponent. We demonstrate the efficiency of our formula by computing the
next-to-nearest neighbour $zz$-correlation function for chain lengths ranging
from two to macroscopic numbers.
