### Article

## Self-consistent T-matrix approach to gap renormalization in quantum magnets with bond disorder

The analytical theory of density of states (DOS) in three-dimensional quantum magnets with the bond disorder is proposed based on the self-consistent T-matrix

approximation (SCTMA). It successfully describes the DOS both for resonant and non-resonant scattering, whose emergence is governed by the ratio of scattering

length and the average distance between impurities, which concentration is denoted as c. Corrections to the quasiparticle band gap in these cases are shown to scale

as c^(2/3) and c, respectively. Moreover, the theory yields a semi-circle form of the DOS for the bound states inside the gap, which results in highly nontrivial DOS in the

intermediate parameter region between the two limiting cases when the band DOS and the semi-circle overlap. Long-wavelength excitations are discussed. In the

resonant regime their damping scales as c^(2/3), which, according to Ioffe-Regel criterion, corresponds to their localization. Applicability of the theory is illustrated by

its quantitative agreement with the recent experimental data on spin-dimer system Ba_(3-x)Sr_xCr_2O_8.