Quantifying quantum chaos through microcanonical distributions of entanglement

Understand

A characteristic feature of "quantum chaotic" systems is that their eigenspectra and eigenstates display universal statistical properties described by random matrix theory (RMT).

• However, eigenstates of local systems also encode structure beyond RMT.
• To capture this, we introduce a quantitative metric for quantum chaos which utilizes the Kullback-Leibler divergence to compare the microcanonical distribution of entanglement entropy (EE) of midspectrum eigenstates with a reference RMT distribution generated by pure random states (with appropriate constraints).
• The metric compares not just the averages of the distributions, but also higher moments.