arXiv:1610.08912 · Journal of Physics A Mathematical and Theoretical

Ground state energy of the δ -Bose and Fermi gas at weak coupling from double extrapolation

Sylvain Prolhac

Published Feb 3, 2017• 25 citations

Abstract

Abstract We consider the ground state energy of the Lieb–Liniger gas with δ interaction in the weak coupling regime γ → 0 . For bosons with repulsive interaction, previous studies gave the expansion e B ( γ ) ≃ γ − 4 γ 3 / 2 / 3 π + ( 1 / 6 − 1 / π 2 ) γ 2 . 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 γ 5 / 2 in the expansion is found to be approximately equal to − 0.001 587 699 865 505 944 989 29 , 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 ( 3 ζ ( 3 ) / 8 − 1 / 2 ) / π 3 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

DOI: 10.1088/1751-8121/aa5e00

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