Nonuniversal properties of the single-particle density of states of 1D system with electron-phonon interactions

Abstract

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 $ω=0$ 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$[K(0)+K^{-1}(0)]ω_0$, where $ω_0$ 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.