2020/11/23 by John Schliemann, João Vitor I. Costa, Joao Vitor I. Costa +2
Mathematics · Physics and Astronomy · #Condensed matter physics #Ergodic theory #Ergodicity #Inflection point #Mathematical analysis #Mathematics #Opinion Dynamics and Social Influence #Physics #Physics of Superconductivity and Magnetism #Quantum many-body systems #Quantum mechanics #Random matrix #Realization (probability) #Spin (aerodynamics) #Statistical physics #Statistics #Thermodynamics #cond-mat.dis-nn
paper · pdf · doi:10.1103/physrevb.103.174203
published as Phys. Rev. B 103, 174203 (2021) · 11 pages, 9 figures. Comments welcome
arxiv created 2020/11/23 · openalex publication_date 2021/05/13 · arxiv updated 2021/05/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
We study the transitions between ergodic and many-body localized phases in spin systems, subject to quenched disorder, including the Heisenberg chain and the central spin model. In both cases systems with common spin lengths 1/2 and 1 are investigated via exact numerical diagonalization and random matrix techniques. Particular attention is paid to the sample-to-sample variance (\mathrm\ensuremathΔsr)2 of the averaged consecutive-gap ratio \ensuremath⟨r\ensuremath⟩ for different disorder realizations. For both types of systems and spin lengths we find a maximum in \mathrm\ensuremathΔsr as a function of disorder strength, accompanied by an inflection point of \ensuremath⟨r\ensuremath⟩, signaling the transition from ergodicity to many-body localization. The critical disorder strength is found to be somewhat smaller than the values reported in the recent literature. Further information about the transitions can be gained from the probability distribution of expectation values within a given disorder realization.