Long-distance behavior of temperature correlation functions in the one-dimensional Bose gas

Abstract

We describe a Bethe ansatz based method to derive, starting from a multiple integral representation, the long-distance asymptotic behavior at finite temperature of the density-density correlation function in the interacting one-dimensional Bose gas. We compute the correlation lengths in terms of solutions of non-linear integral equations of the thermodynamic Bethe ansatz type. Finally, we establish a connection between the results obtained in our approach with the correlation lengths stemming from the quantum transfer matrix method.

40 pages, 4 figures

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• Separation of variables bases for integrable $g{l}_{\mathcal{M}|\mathcal{N}}$ and Hubbard models
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• Temperature-driven crossover in the Lieb-Liniger model
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• Correlation functions by Separation of Variables: the XXX spin chain
• Correlation functions for open XXZ spin 1/2 quantum chains with unparallel boundary magnetic fields
• Low-density limit of dynamical correlations in the Lieb-Liniger model
• Quantum corrections to the classical field approximation for one-dimensional quantum many-body systems in equilibrium
• Determinant formula for the field form factor in the anyonic Lieb-Liniger model
• The LeClair-Mussardo series and nested Bethe Ansatz
• On correlation functions for the open XXZ chain with non-longitudinal boundary fields : the case with a constraint
• Non-Equilibrium Steady State of the Lieb-Liniger model: multiple-integral representation of the time evolved many-body wave-function
• Space-like asymptotics of the thermal two-point functions of the XXZ spin-1/2 chain