# Finite-size scaling of pseudo-critical point distributions in the random transverse-field Ising chain

## TL;DR

This paper investigates the distribution of pseudo-critical points in a one-dimensional random quantum magnet, revealing a log-normal distribution with specific scaling behaviors related to the infinite randomness fixed point.

## Contribution

It introduces three methods to define pseudo-critical points and demonstrates their consistent log-normal distribution and scaling properties in the random transverse-field Ising chain.

## Key findings

- Pseudo-critical points follow a log-normal distribution.
- The width scales as L^{-1/2} with system size.
- The average shift scales as L^{-1}.

## Abstract

We study the distribution of finite size pseudo-critical points in a one-dimensional random quantum magnet with a quantum phase transition described by an infinite randomness fixed point. Pseudo-critical 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 pseudo-critical transverse fields, where the width scales as $L^{-1/\nu}$ with $\nu=2$ and the shift of the average value scales as $L^{-1/\nu_{typ}}$ with $\nu_{typ}=1$, which we related to the scaling of average and typical quantities in the critical region.