Effects of Noncommuting Charges in Quantum Information and Thermodynamics

Abstract

The advancement of quantum theory is rooted in challenging established assumptions. This trend persists as quantum theory extends into other fields, including thermodynamics. One such assumption in thermodynamics is that conserved quantities, known as charges, commute. Lifting this assumption has led to a new subfield, noncommuting charges, at the intersection of quantum information and quantum thermodynamics. The work presented in this thesis identifies various effects of noncommuting charges and extends the topic to many-body physics and experiments.

Initially, the field’s findings were conveyed in abstract information-theoretic terms. To transition these findings to experimental practice and tie them to many-body physics, constructing relevant Hamiltonians is essential. We introduce a method for constructing Hamiltonians that globally conserve noncommuting quantities while facilitating their local transport.

Having demonstrated the testability of noncommuting-charge physics, we aim to delineate its effects. To do so, we construct analogous models that differ in whether their charges commute. We find that noncommuting models exhibit higher entanglement entropies. Since entanglement accompanies thermalization, our result challenges previous assertions that charges’ noncommutation hinders thermalization.

Motivated by understanding noncommuting charges’ effects on entanglement, we introduce them into monitored quantum circuits. Monitored quantum circuits typically transition from a highly entangled volume-law phase to a less entangled area-law phase as one increases the rate of measurements. This holds for monitored quantum circuits with no charges and commuting ones. We find that by introducing noncommuting charges into monitored quantum circuits, the area-law phase becomes replaced with a critical phase. Since critical phases are characterized by long-range entanglement, this result reinforces entanglement enhancement by noncommuting charges.

Finally, we revisit the puzzle of whether noncommuting charges promote or hinder thermalization. Most quantum many-body systems thermalize; some don’t. In those that don’t, what effect do noncommuting charges have? One type of system that does not thermalize is a system whose Hamiltonian has so-called dynamical symmetries (or spectrum-generating algebras). We find that noncommuting charges promote thermalization by reducing the dynamical symmetries in a system.