Distributions of gaps and end-to-end correlations in random transverse-field Ising spin chains

TL;DR

This paper extends a real space renormalization-group method to analyze the distributions of energy gaps and end-to-end correlations in long random transverse-field Ising chains, confirming predictions with numerical data.

Contribution

It provides detailed distribution analyses of energy gaps and correlations in disordered chains, combining analytic scaling with numerical verification.

Findings

Distributions match finite size scaling predictions

Numerical data agree with analytic results

Enhanced understanding of boundary effects in disordered chains

Abstract

A previously introduced real space renormalization-group treatment of the random transverse-field Ising spin chain is extended to provide detailed information on the distribution of the energy gap and the end-to-end correlation function for long chains with free boundary conditions. Numerical data, using the mapping of the problem to free fermions, are found to be in good agreement with the analytic finite size scaling predictions.