Exact emergent quantum state designs from quantum chaotic dynamics

Understand

We present exact results on a novel kind of emergent random matrix universality that quantum many-body systems at infinite temperature can exhibit.

• Specifically, we consider an ensemble of pure states supported on a small subsystem, generated from projective measurements of the remainder of the system in a local basis.
• We rigorously show that the ensemble, derived for a class of quantum chaotic systems undergoing quench dynamics, approaches a universal form completely independent of system details: it becomes uniformly distributed in Hilbert space.
• This goes beyond the standard paradigm of quantum thermalization, which dictates that the subsystem relaxes to an ensemble of quantum states that reproduces the expectation values of local observables in a thermal mixed state.