Lieb-Liniger Delta Bose Gas

Coupling γ = c/n 1.00

γ→0: BEC limit | γ→∞: Tonks-Girardeau

N particles 4

Temperature T/T_F 0.00

Ground state energy E₀/E_free—

Sound velocity v_s/v_F—

Compressibility κ—

Regime—

Lieb-Liniger (1963): H = −Σ∂²/∂xᵢ² + 2c Σ δ(xᵢ−xⱼ) on a ring of length L.

Exact solution via Bethe ansatz: quasi-momenta {kⱼ} satisfy Bethe equations
e^{ikⱼL} = Π_{l≠j} (kⱼ−k_l + ic)/(kⱼ−k_l − ic)

γ→∞ (Tonks): fermionized gas — momentum distribution broadens. γ→0: BEC, sharp peak at k=0.