Singularities and Pseudogaps in the Density of States of Peierls Chains

We develop a nonperturbative method to calculate the density of states (DOS) ρ(ω) of the fluctuating gap model describing the low-energy physics of electrons on a disordered Peierls chain. For a real order parameter field we calculate ρ(0) (i.e., the DOS at the Fermi energy) exactly as a functional of the disorder for a chain of finite length L. Averaging ρ(0) with respect to a Gaussian probability distribution of the fluctuating Peierls order parameter, we show that for L→∞ the average 〈ρ(0)〉 diverges for any finite value of the correlation length above the Peierls transition. Pseudogap behavior emerges only if the Peierls order parameter is finite and sufficiently large.