Griffiths-McCoy singularities in random quantum spin chains: Exact resultsthrough renormalization

The Ma-Dasgupta-Hu renormalization group (RG) scheme is used to study singu lar quantities in the Griffiths phase of random quantum spin chains. For th e random transverse-field Ising spin chain we have extended Fisher's analyt ical solution to the off-critical region and calculated the dynamical expon ent exactly. Concerning other random chains we argue by scaling considerati ons that the RC method generally becomes asymptotically tract fur large tim es, both at the critical point and in the whole Griffiths phase. This state ment is checked via numerical calculations on the random Heisenberg and qua ntum Potts models by the density matrix renormalization group method.