From Thermalization to Multifractality: Spin-Spin Correlation in Disordered $SU(2)$-Invariant 1D Heisenberg Spin Chains
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| Format: | Preprint |
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2025
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| _version_ | 1866915421822648320 |
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| author | Giri, Debasmita Siegl, Julian Schliemann, John |
| author_facet | Giri, Debasmita Siegl, Julian Schliemann, John |
| contents | 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 ($D_2=0$). |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_00573 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | From Thermalization to Multifractality: Spin-Spin Correlation in Disordered $SU(2)$-Invariant 1D Heisenberg Spin Chains Giri, Debasmita Siegl, Julian Schliemann, John Disordered Systems and Neural Networks 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 ($D_2=0$). |
| title | From Thermalization to Multifractality: Spin-Spin Correlation in Disordered $SU(2)$-Invariant 1D Heisenberg Spin Chains |
| topic | Disordered Systems and Neural Networks |
| url | https://arxiv.org/abs/2508.00573 |