Critical level spacing distribution in long-range hopping Hamiltonians

Abstract

The nearest level spacing distribution $P_c(s)$ of $d$-dimensional disordered models ($d=1$ and 2) with long-range random hopping amplitudes is investigated numerically at criticality. We focus on both the weak ($b^d\gg 1$) and the strong ($b^d\ll 1$) coupling regime, where the parameter $b^{-d}$ plays the role of the coupling constant of the model. It is found that $P_c(s)$ has the asymptotic form $P_c(s)\sim \exp [-A_d{s}^{\alpha }]$ for $s\gg 1$, with the critical exponent $\alpha =2-a_d/b^d$ in the weak coupling limit and $\alpha =1+c_d{b}^d$ in the case of strong coupling.

EPL style, 7 pages, 4 .eps figures, to be published in Europhys. Lett

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Cited by in corpus (7)

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• Entanglement Properties of Disordered Quantum Spin Chains with Long-Range Antiferromagnetic Interactions
• A critical Dyson hierarchical model for the Anderson localization transition
• Many-Body Localization Transition in Random Quantum Spin Chains with Long-Range Interactions
• Two-level correlation function of critical random-matrix ensembles
• On the multifractal dimensions and statistical properties of critical ensembles characterized by the three classical Wigner-Dyson symmetry classes
• Statistical properties of the critical eigenstates in power-law random banded matrices across the band