Abstract
We consider the ground state energy of the Lieb–Liniger gas with δ interaction in the weak coupling regime . For bosons with repulsive interaction, previous studies gave the expansion . Using a numerical solution of the Lieb–Liniger integral equation discretized with M points and finite strength γ of the interaction, we obtain very accurate numerics for the next orders after extrapolation on M and γ. The coefficient of in the expansion is found to be approximately equal to , accurate within all digits shown. This value is supported by a numerical solution of the Bethe equations with N particles, followed by extrapolation on N and γ. It was identified as by G Lang. The next two coefficients are also guessed from the numerics. For balanced spin 1/2 fermions with attractive interaction, the best result so far for the ground state energy has been . An analogue double extrapolation scheme leads to the value for the coefficient of .
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