Sensitivity of the spectral form factor to short-range level statistics

Area of Science:

• Quantum mechanics
• Statistical physics

Background:

• The spectral form factor (SFF) is a key tool for analyzing quantum system level statistics.
• Current interpretations often link early-time SFF behavior to large-separation two-point correlations.

Purpose of the Study:

• To challenge the restrictive interpretation of SFF early-time behavior.
• To investigate how self-correlation and two-point correlation functions constrain the SFF.
• To propose a novel probe for quantum ergodicity that mitigates these constraints.

Main Methods:

• Theoretical analysis of spectral form factor properties.
• Derivation of constraints imposed by correlation functions on the integrated SFF.
• Development and application of a modified probe for SFF analysis.

Main Results:

• The self-correlation imposes a significant constraint on the time-integrated SFF.
• Each expansion coefficient of the two-point correlation function constrains the weighted time-integrated SFF.
• A new probe successfully removes the self-correlation constraint.

Conclusions:

• The standard interpretation of SFF is too restrictive due to self-correlation effects.
• The proposed probe offers a more robust method for studying quantum ergodicity.
• The new probe is validated on models of incomplete spectra and many-body localization.