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

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.

23 pages, 2 figures, v2: minor modifications and references added

References in corpus (14)

• Dynamical density-density correlations in the one-dimensional Bose gas
• Form factors in finite volume II:disconnected terms and finite temperature correlators
• Exact exponents of edge singularities in dynamic correlation functions of 1D Bose gas
• Relaxation dynamics in the gapped XXZ spin-1/2 chain
• Algebraic Bethe ansatz approach to the asymptotic behavior of correlation functions
• Exact three-body local correlations for excited states of the 1D Bose gas
• Mean values of local operators in highly excited Bethe states
• Yang-Yang thermometry and momentum distribution of a trapped one-dimensional Bose gas
• Factorization of the finite temperature correlation functions of the XXZ chain in a magnetic field
• Long-distance behavior of temperature correlation functions in the one-dimensional Bose gas
• Three-body local correlation function in the Lieb-Liniger model: bosonization approach
• A note on the spin-1/2 XXZ chain concerning its relation to the Bose gas
• Correlation functions of one-dimensional bosons at low temperature
• Bethe Ansatz Matrix Elements as Non-Relativistic Limits of Form Factors of Quantum Field Theory

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