☆ 4.6 Article

Local correlations in the 1D Bose gas from a scaling limit of the XXZ chain

JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT (2011)

Journal

JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT

Volume -, Issue -, Pages -

Publisher

IOP PUBLISHING LTD

DOI: 10.1088/1742-5468/2011/11/P11017

Keywords

correlation functions; form factors; quantum integrability (Bethe ansatz)

Categories

Mechanics Physics, Mathematical

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Abstract

We consider the K-body local correlations in the (repulsive) 1D Bose gas for general K, both at finite size and in the thermodynamic limit. Concerning the latter we develop a multiple integral formula which applies for arbitrary states of the system with a smooth distribution of Bethe roots, including the ground state and finite-temperature Gibbs states. In the cases K <= 4 we perform the explicit factorization of the multiple integral. In the case of K = 3 we obtain the recent result of Kormos et al, whereas our formula for K = 4 is new. Numerical results are presented as well.

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