تقرير
Spectral Analysis of the Quantum Random Energy Model
| العنوان: | Spectral Analysis of the Quantum Random Energy Model |
|---|---|
| المؤلفون: | Manai, Chokri, Warzel, Simone |
| سنة النشر: | 2022 |
| المجموعة: | Mathematics Condensed Matter Mathematical Physics |
| مصطلحات موضوعية: | Mathematical Physics, Condensed Matter - Disordered Systems and Neural Networks, Mathematics - Probability, 60K35, 82B44, 82D30 |
| الوصف: | The Quantum Random Energy Model (QREM) is a random matrix of Anderson-type which describes effects of a transversal magnetic field on Derrida's spin glass. The model exhibits a glass phase as well as a classical and a quantum paramagnetic phase. We analyze in detail the low-energy spectrum and establish a localization-delocalization transition for the corresponding eigenvectors of the QREM. Based on a combination of random matrix and operator techniques as well as insights in the random geometry, we derive next-to-leading order asymptotics for the ground-state energy and eigenvectors in all regimes of the parameter space. Based on this, we also deduce the next-to-leading order of the free energy, which turns out to be deterministic and on order one in the system size in all phases of the QREM. As a result, we determine the nature of the fluctuations of the free energy in the spin glass regime. Comment: Typos and presentation corrected, refernces added |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1007/s00220-023-04743-4 |
| URL الوصول: | http://arxiv.org/abs/2202.00334 |
| رقم الأكسشن: | edsarx.2202.00334 |
| قاعدة البيانات: | arXiv |
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