Luttinger parameter ($K$)

The Luttinger parameter $K$ characterizes interactions and correlation exponents in a low-energy Luttinger liquid. In one common spinless convention,The parameter $v$ sets the collective-mode speed, while $K$ balances the conjugate phase and density stiffnesses. For noninteracting spinless fermions $K=1$; repulsive and attractive interactions commonly move it below and above one within this convention. Spinful models have separate charge and spin sectors. Normalization and boundary conditions must accompany comparisons between formulas.