Excitation spectra of quantum matter without quasiparticles II: random t-J model

We study the low frequency spectrum of the deconfined critical state of t-J model with random exchange. The analysis is carried out in the large M limit of models with global SU(M) spin symmetry. The spectral density is computed by numerical analysis of the saddle point equations on the real frequency axis at zero temperature (T). The asymptotic low frequency behavior is found to be in excellent agreement with the scaling dimensions of irrelevant operators which perturb the conformally invariant critical states. The low T dependence of the resistivity of the t-J model is also determined by these irrelevant operators: the operator associated with the time-reparameterization mode leads to a resistivity∼T. In the large M limit, we also find a less irrelevant operator which leads to a resistivity~T^a where a<1, but with a prefactor which is significantly smaller than that of the ~T term.