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13 Calculation of multifractal dimensions in spin chains

E. Bogomolny, Y. Y. Atas, E. Bogomolny

Published Jan 1, 2014• 32 citations
OpenAlex

Abstract

It was demonstrated in [Phys. Rev. E 86, 021104, (2012)], that the ground-state wave functions for a large variety of one-dimensional spin-1/2 models are multifractals in the natural spin-z basis. We present here the details of analytical derivations and numerical confirmations of these results.

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From Thermalization to Multifractality: Spin-Spin Correlation in Disordered SU(2)SU(2)SU(2)-Invariant 1D Heisenberg Spin Chains
We investigate spin correlations in one-dimensional SU(2)SU(2)SU(2)-invariant Heisenberg chains with exchange disorder for spin lengths S=1/2S=1/2S=1/2 and S=1S=1S=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, D2≈0.37−0.39D_2\approx 0.37-0.39D2​≈0.37−0.39, confirming the stability of a multifractal regime that is distinct from both the ergodic limit (D2=1D_2=1D2​=1) and the fully localized limit (D2=0D_2=0D2​=0).
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