Exact Results in Quantum Theory & Gravity

The Lieb-Liniger model describes bosonic particles in one dimension that interact via a delta-function interaction. This model belongs to a small group of integrable models. It was exactly solved by Lieb and Liniger in 1963 using the Bethe ansatz. Despite that, extracting explicit analytical results for the quantities of interest is a formidable task. In this talk, we will overview several new exact results for the Lieb-Liniger model. The first is the perturbative expansion for the ground-state energy, which is obtained using the techniques of experimental mathematics. The second is the result for the boundary energy of the system, which was only approximatively solved by Gaudin in 1971. The third is the low-energy spectrum of elementary excitations. Finally, we will derive and discuss the difference-differential equation for the expectation values of the conserved charges of the model in the ground state, enabling one to obtain explicit analytical results.
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