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

Published

July 16, 2018

Author(s)

Paraj T. Bhattacharjee, Victor L. Quito, Sergey V. Syzranov

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 $\propto 1/r^\alpha$ 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 $R_2(\omega)$ 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 $R_2(\omega,V)=A_3\frac{\omega}{\omega_V}$ for small frequencies $\omega\ll\omega_V$ and $R_2(\omega,V)=1-(\alpha-d)A_{1}\left(\frac{\omega_V}{\omega}\right)^\frac{d}{\alpha} -A_2\left(\frac{\omega_V}{\omega}\right)^2$ for large frequencies $\omega\gg\omega_V$, where $\omega_V\propto V^{-\frac{\alpha}{d}}$ is the characteristic matrix element of excitation hopping in a system of volume $V$, and $A_1$, $A_2$ and $A_3$ 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.

Citation

Physical Review B

Pub Type

Journals

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Keywords

Disordered systems

Citation

Bhattacharjee, P. , Quito, V. and Syzranov, S. (2018), Energy-level statistics in strongly disordered systems with power-law hopping, Physical Review B, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=925681 (Accessed October 8, 2025)