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

Area of Science:

• Condensed Matter Physics
• Quantum Mechanics
• Disordered Systems

Background:

• Neutral excitations in disordered electronic materials and ultracold particle systems exhibit long-range interactions.
• These quasiparticles, like neutral dipolar excitations, influence local observables and energy transport.
• Understanding their behavior is crucial for materials science and quantum simulations.

Purpose of the Study:

• To investigate the energy-level statistics of quasiparticles in disordered systems with power-law hopping.
• To compute the energy-level correlation function in the limit of strong disorder.
• To explore potential experimental methods for observing these statistical properties.

Main Methods:

• Theoretical analysis of quasiparticles with a power-law hopping Hamiltonian (proportional to 1/r^alpha) in a strong random potential.
• Calculation of the energy-level correlation function R_2(omega) for a finite system.
• Analysis in the limit of sufficiently strong disorder.

Main Results:

• Energy-level correlations exhibit Wigner-Dyson statistics at small energy differences.
• Formulas for the energy-level correlation function R_2(omega, V) derived for both small and large frequencies in the very strong disorder limit.
• Characteristic matrix element of excitation hopping (omega_V) depends on system volume (V) and hopping exponent (alpha/d).

Conclusions:

• The derived energy-level correlation function provides a direct route for experimental verification.
• Measurements of ac conductance correlations can be used to observe these quantum phenomena.
• Findings are relevant for understanding energy transport and correlations in disordered quantum systems.