Adaptive Density-Matrix Renormalization-Group study of the disordered antiferromagnetic spin-1/2 Heisenberg chain

TL;DR

This study uses an adaptive density-matrix renormalization-group method to analyze disordered antiferromagnetic spin-1/2 chains, confirming strong-disorder predictions and revealing universal correlation distributions without logarithmic corrections.

Contribution

It applies a novel adaptive DMRG approach to disordered chains, providing detailed correlation statistics and confirming theoretical predictions with high accuracy.

Findings

Agreement with strong-disorder renormalization group predictions

No logarithmic corrections in bulk and end-to-end correlations

Universal, disorder-independent distribution of bulk correlations

Abstract

Using the recently introduced adaptive density-matrix renormalization-group method, we study the many spin-spin correlations of the spin-$1/2$ antiferromagnetic Heisenberg chain with random coupling constants, namely, the mean value of the bulk and of the end-to-end correlations, the typical value of the bulk correlations, and the distribution of the bulk correlations. Our results are in striking agreement with the predictions of the strong-disorder renormalization group method. We do not find any hint of logarithmic corrections neither in the bulk average correlations, which were recently reported by Shu et al. [Phys. Rev. B 94,174442 (2016)], nor in the end-to-end average correlations. We report computed the existence of logarithmic correction on the end-to-end correlations of the clean chain. Finally, we have determined that the distribution of the bulk correlations, when properly rescaled by an associated Lyapunov exponent, is a narrow and universal (disorder-independent) probability function.