Finite-size scaling of pseudocritical point distributions in the random transverse-field Ising chain

We study the distribution of finite-size pseudocritical points in a one-dimensional random quantum magnet with a quantum phase transition described by an infinite randomness fixed point. Pseudocritical points are defined in three different ways: the position of the maximum of the average entanglement entropy, the scaling behavior of the surface magnetization, and the energy of a soft mode. All three lead to a log-normal distribution of the pseudocritical transverse fields, where the width scales as L-1/nu with nu=2 and the shift of the average value scales as L-typ(-1/nu) with nu(typ)=1, which we related to the scaling of average and typical quantities in the critical region.