Understanding many-body physics in one dimension from the Lieb–Liniger model*
Jiang Yu-Zhua),b), Chen Yang-Yanga),b), Guan Xi-Wena),b)†
       
Densities and dressed energies of pseudo momenta for the ground state. (a) Solid lines: the dimensionless densities of the pseudo momenta, ρ̃ ( k ) = ρ ( k )/ c obtained from Eq. ( 23 ); dotted lines: the corresponding dimensionless hole densities, ρ̃ h( k ) = ρ h( k )/ c . When the coupling strength is small, the distribution function ρ̃ meets a semi-circle law ( 27 ). For the strong coupling limit, i.e., γ ≫ 1, the distribution function gradually becomes flatter and flatter, and approaches ρ ( k ) ≈ 1/2 π . (b) Dimensionless dressed energy is defined by ε̃ ( k ) = ε ( k )/ c 3, which is obtained from the dressed energy equation ( 64 ).