A Numerical Study of the Random Transverse-Field Ising Spin Chain

TL;DR

This paper numerically investigates the critical and disordered phases of the random transverse-field Ising chain, confirming analytical predictions and providing new insights into probability distributions and scaling functions.

Contribution

It offers a numerically exact solution for large system sizes using a fermion mapping, validating and extending previous analytical results.

Findings

Confirmed analytical predictions about the critical region

Provided new results for probability distributions

Analyzed scaling functions in the disordered phase

Abstract

We study numerically the critical region and the disordered phase of the random transverse-field Ising chain. By using a mapping of Lieb, Schultz and Mattis to non-interacting fermions, we can obtain a numerically exact solution for rather large system sizes, $L \le 128$. Our results confirm the striking predictions of earlier analytical work and, in addition, give new results for some probability distributions and scaling functions.