It was well known that for (1+1)d CFT(z=1) case, we can use the tool of conformal map to derive the formula of entanglement entropy for a finite interval: S ~ $c \log L$. L is the length of the interval.(allow me to be sloppy, i neglect the coefficient and cutoff in the formula).
My question is: is there a derivation in literature or in your mind that shows the entanglement entropy formula for other dynamical critical exponent? for example z=2(quadratic dispersion) or z=3, in a (1+1)d field theory model.
I'd like to know how the formula looks like, $\log L$ or $L^{\alpha}$ for some exponent $\alpha$ determined by the universality class of the theory.