Multifractal orthogonality catastrophe in one-dimensional random quantum critical points

We study the response of random singlet quantum critical points to local\nperturbations. Despite being insulating, these systems are dramatically\naffected by a local cut in the system, so that the overlap $G=\\left|\\langle\n\\Psi_B |\\Psi_A \\rangle\\right|$ of the groundstate wave functions with and\nwithout a cut vanishes algebraically in the thermodynamic limit. We analyze\nthis Anderson orthogonality catastrophe in detail using a real-space\nrenormalization group approach. We show that both the typical value of the\noverlap G and the disorder average of $G^\\alpha$ with $\\alpha>0$ decay as\npower-laws of the system size. In particular, the disorder average of\n$G^\\alpha$ shows a "multifractal" behavior, with a non-trivial limit $\\alpha\n\\to \\infty$ that is dominated by rare events. We also discuss the case of more\ngeneric local perturbations and generalize these results to local quantum\nquenches.\n