{title2=$K$}

The <Luttinger parameter> $K$ characterizes interactions and correlation exponents in a low-energy <Luttinger liquid>. In one common spinless convention,
$$
H=\frac{\hbar v}{2\pi}\int\left[K(\partial_x\theta)^2+K^{-1}(\partial_x\phi)^2\right]dx.
$$
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.


 Luttinger parameter (source code)