A noncommuting charge puzzle

The assumption that conserved quantities, also known as charges, commute underpins many basic physics derivations, such as that of the thermal state's form and Onsager coefficients. Yet, the failure of operators to commute plays a key role in quantum theory, e.g., underlying uncertainty relations. Recently, the study of systems with noncommuting charges has emerged as a growing subfield of quantum many-body physics and revealed a conceptual puzzle: noncommuting charges can hinder thermalization in some ways, yet promote it in others.

In this talk, we address this puzzle in two distinct settings. First, we introduce noncommuting charges into monitored quantum circuits—a toolbox for studying entanglement dynamics. Numerical results reveal a critical phase with long-range entanglement, replacing the area-law phase typically observed in such circuits. This enhanced entanglement indicates noncommuting charges promote entanglement generation, which accompanies thermalization. Second, we consider systems with dynamical symmetries, which are known to violate the Eigenstate Thermalization Hypothesis (ETH), leading to non-stationary dynamics and preventing equilibration, let alone thermalization. We demonstrate that each pair of dynamical symmetries corresponds to a specific charge. Importantly, introducing new charges that do not commute with the existing charges disrupts the associated non-stationary dynamics, thereby facilitating thermalization.

 

Together, these results shed light on the complex interplay between noncommuting charges, entanglement dynamics, and thermalization in quantum many-body systems.