Instanton calculation of the density of states of disordered Peierls chains

We use the optimal fluctuation method to find the density of electron states inside the pseudogap in disordered Peierls chains. The electrons are described by the one-dimensional Dirac Hamiltonian with randomly varying mass (the Fluctuating Gap Model). We establish a relation between the disorder average in this model and the quantum-mechanical average for a certain double-well problem. We show that the optimal disorder fluctuation, which has the form of a soliton-antisoliton pair, corresponds to the instanton trajectory in the double-well problem. We use the instanton method developed for the double-well problem to find the contribution to the density of states from disorder realizations close to the optimal fluctuation.