From the sinh-Gordon field theory to the one-dimensional Bose gas: exact local correlations and full counting statistics
arXiv:1807.06869 · doi:10.1088/1742-5468/aaeb48
Abstract
We derive exact formulas for the expectation value of local observables in a one-dimensional gas of bosons with point-wise repulsive interactions (Lieb-Liniger model). Starting from a recently conjectured expression for the expectation value of vertex operators in the sinh-Gordon field theory, we derive explicit analytic expressions for the one-point -body correlation functions in the Lieb-Liniger gas, for arbitrary integer . These are valid for all excited states in the thermodynamic limit, including thermal states, generalized Gibbs ensembles and non-equilibrium steady states arising in transport settings. Our formulas display several physically interesting applications: most prominently, they allow us to compute the full counting statistics for the particle-number fluctuations in a short interval. Furthermore, combining our findings with the recently introduced generalized hydrodynamics, we are able to study multi-point correlation functions at the Eulerian scale in non-homogeneous settings. Our results complement previous studies in the literature and provide a full solution to the problem of computing one-point functions in the Lieb Liniger model.
26 pages, 4 figures; v2: minor revision and figure added
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