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arXiv:1211.4200 · Physical Review A

Correlation lengths of the repulsive one-dimensional Bose gas

Ovidiu I. Pâţu, Andreas Klümper

Published Sep 19, 2013• 25 citations

Abstract

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)] nonlinear integral equations which are easily implementable numerically.

DOI: 10.1103/physreva.88.033623

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