We investigate the large-distance asymptotic behavior of the static
density-density and field-field correlation functions in the one-dimensional
Bose gas at finite temperature. The asymptotic expansions of the Bose gas
correlators are obtained performing a specific continuum limit in the similar
low-temperature expansions of the longitudinal and transversal correlation
functions of the XXZ spin chain. In the lattice system the correlation lengths
are computed as ratios of the largest and next-largest eigenvalues of the XXZ
spin chain quantum transfer matrix. In both cases, lattice and continuum, the
correlation lengths are expressed in terms of solutions of Yang-Yang type [C.N.
Yang and C.P. Yang, J.Math.Phys. 10, 1151 (1969)] non-linear integral equations
which are easily implementable numerically.Comment: 35+9 pages, 7 figures, RevTeX 4.