Deep thermalization under charge-conserving quantum dynamics

Understand

"Deep thermalization" describes the emergence of universal wavefunction distributions in quantum many-body dynamics, appearing on a local subsystem upon measurement of its environment.

• In this work, we study in detail the effect of continuous internal symmetries and associated conservation laws on deep thermalization.
• Concretely, we consider quantum spin systems with a $U(1)$ symmetry associated with the conservation of magnetization (or `charge'), and analyze how the choice of initial states (specifically, their degree of charge fluctuations) and the choice of measurement basis (specifically, whether or not it can reveal information about the local charge density) determine the ensuing universal wavefunction distributions.
• We put forth a universal ansatz for the limiting form of the projected ensemble, motivated by maximum-entropy principles rooted in statistical physics and quantum information theory.