Title | Energy-level statistics in strongly disordered systems with power-law hopping |

Publication Type | Journal Article |

Year of Publication | 2018 |

Authors | Titum, P, Quito, VL, Syzranov, SV |

Journal | Phys. Rev. |

Volume | B |

Issue | 98 |

Pages | 014201 |

Date Published | 2018/07/16 |

Abstract | Motivated by neutral excitations in disordered electronic materials and systems of trapped ultracold particles with long-range interactions, we study energy-level statistics of quasiparticles with the power-law hopping Hamiltonian ∝1/rα in a strong random potential. In solid-state systems such quasiparticles, which are exemplified by neutral dipolar excitations, lead to long-range correlations of local observables and may dominate energy transport. Focussing on the excitations in disordered electronic systems, we compute the energy-level correlation function R2(ω) in a finite system in the limit of sufficiently strong disorder. At small energy differences the correlations exhibit Wigner-Dyson statistics. In particular, in the limit of very strong disorder the energy-level correlation function is given by R2(ω,V)=A3ωωV for small frequencies ω≪ωV and R2(ω,V)=1−(α−d)A1(ωVω)dα−A2(ωVω)2 for large frequencies ω≫ωV, where ωV∝V−αd is the characteristic matrix element of excitation hopping in a system of volume V, and A1, A2 and A3 are coefficient of order unity which depend on the shape of the system. The energy-level correlation function, which we study, allows for a direct experimental observation, for example, by measuring the correlations of the ac conductance of the system at different frequencies. |

URL | https://arxiv.org/abs/1803.11178 |

DOI | 10.1103/PhysRevB.98.014201 |