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

TL;DR

This paper investigates how electron-phonon interactions influence the single-particle density of states in a 1D spinful Tomonaga-Luttinger liquid, revealing nonuniversal features such as a shifted peak and power-law suppression near zero energy.

Contribution

It introduces a model with frequency-dependent charge sector parameter $K_c$ to analyze DOS, highlighting nonuniversal properties caused by phonon interactions.

Findings

DOS shows power-law suppression near zero energy with exponent > 1.

A peak in DOS appears at a frequency scaling with $K(0)+K^{-1}(0)$ and phonon frequency.

Peak position shifts with phonon frequency, not aligning with the phonon frequency itself.

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 $\omega=0$ 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.