Numerical renormalization-group study of spin correlations in one-dimensional random spin chains

TL;DR

This study uses an extended numerical renormalization group method to analyze spin correlations in one-dimensional random spin chains, confirming algebraic decay in AF chains and logarithmic decay in mixed FM-AF chains.

Contribution

It introduces an improved real-space renormalization scheme that accurately captures local multiplet excitations in disordered spin chains.

Findings

AF chains exhibit $1/r^2$ decay of correlations.

Mixed FM-AF chains show slower, logarithmic decay.

Distribution functions of correlations differ between AF and FM-AF chains.

Abstract

We calculate the ground-state two-spin correlation functions of spin-1/2 quantum Heisenberg chains with random exchange couplings using the real-space renormalization group scheme. We extend the conventional scheme to take account of the contribution of local higher multiplet excitations in each decimation step. This extended scheme can provide highly accurate numerical data for large systems. The random average of staggered spin correlations of the chains with random antiferromagnetic (AF) couplings shows algebraic decay like $1/r^2$, which verifies the Fisher's analytic results. For chains with random ferromagnetic (FM) and AF couplings, the random average of generalized staggered correlations is found to decay more slowly than a power-law, in the form close to $1/\ln(r)$. The difference between the distribution functions of the spin correlations of the random AF chains and of the random FM-AF chains is also discussed.