From Thermalization to Multifractality: Spin-Spin Correlation in Disordered $SU(2)$-Invariant 1D Heisenberg Spin Chains

TL;DR

This paper studies how spin correlations in disordered 1D Heisenberg chains transition from ergodic to multifractal phases, revealing a stable multifractal regime with specific correlation dimensions.

Contribution

It demonstrates the existence of a stable multifractal phase in disordered Heisenberg chains and characterizes its properties through finite-size scaling analysis.

Findings

Eigenmodes are delocalized in weak disorder, indicating ergodicity.

Strong disorder induces a multifractal phase with exponential decay of correlations.

Correlation dimension D2 is approximately 0.37-0.39, confirming multifractality.

Abstract

We investigate spin correlations in one-dimensional $SU(2)$-invariant Heisenberg chains with exchange disorder for spin lengths $S=1/2$ and $S=1$. In the weak-disorder regime, the eigenmodes of the spin-spin correlation matrix are delocalized, consistent with ergodic behavior. Under strong disorder, the system enters a quasi-localized multifractal phase characterized by exponentially decaying, dimer-like spin correlations. Finite-size scaling of the inverse participation ratios of the correlation-matrix eigenmodes yields a correlation dimension, $D_2\approx 0.37-0.39$, confirming the stability of a multifractal regime that is distinct from both the ergodic limit ($D_2=1$) and the fully localized limit ($D_2=0$).