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arXiv · 1211.4200

Correlation lengths of the repulsive one-dimensional Bose gas

Ovidiu I. Patu·Andreas Klumper
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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)] non-linear integral equations which are easily implementable numerically.

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Ovidiu I. Patu, Andreas Klumper. 2013-10-02. Correlation lengths of the repulsive one-dimensional Bose gas. https://doi.org/10.1103/physreva.88.033623

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