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

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We have calculated the single-particle density of states (DOS) for a model of spinfull Tomonaga-Luttinger liquid with frequency dependent parameter Kc of the charge sector (and Kₛ=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)]ω₀, where ω₀ 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.