Self-consistent T-matrix approach to Bose-glass in one dimension

Based on the self-consistent T-matrix approximation (SCTMA), the Mott insulator – Bose-glass phase transition of one-dimensional noninteracting bosons subject to binary disorder is considered. The results obtained differ essentially from the conventional case of box distribution of the disorder. The Mott insulator – Bose-glass transition is found to exist at arbitrary strength of the impurities. The single particle density of states is calculated within the frame of SCTMA, numerically, and (for infinite disorder strength) analytically. A good agreement is reported among all three methods. We speculate that certain types of the interaction may lead to the Bose-glass – superfluid transition absent in our theory.