Nonuniversal properties of the single-particle density of states of 1D   system with electron-phonon interactions
  We have calculated the single-particle density of states (DOS) for a model of spinfull Tomonaga-Luttinger liquid with frequency dependent parameter $K_c$ of the charge sector (and $K_s=1$ of spin sector).Such frequency dependence may originate from interactions withoptical phonons.DOS exhibits a power-low suppressed asymptotic behaviour near $\omega=0$ with exponent largerthan one, in agreement with previous results. For larger frequencies, but stillnot far away from the origin,DOS exhibits a peak, the position of which scales as$[K(0)+K^{-1}(0)]\omega_0$, where $\omega_0$ is the characteristic phononfrequency. The position of the peak decreases as the phonon'sfrequency becomes smaller. It is interesting that the peak of DOS does not coincide with the characteristic phonon frequency. 
Emiliano Papa