Noncommuting conserved charges in quantum many-body thermalization

Abstract

In statistical mechanics, a small system exchanges conserved charges-heat, particles, electric charge, etc.-with a bath. The small system thermalizes to the canonical ensemble, or the grand canonical ensemble, etc., depending on the charges. The charges are usually represented by operators assumed to commute with each other. This assumption was removed within quantum-informationtheoretic (QI-theoretic) thermodynamics recently. The small system's long-time state was dubbed "the non-Abelian thermal state (NATS)." We propose an experimental protocol for observing a system thermalize to the NATS. We illustrate with a chain of spins, a subset of which form the system of interest. The conserved charges manifest as spin components. Heisenberg interactions push the charges between the system and the effective bath, the rest of the chain. We predict longtime expectation values, extending the NATS theory from abstract idealization to finite systems that thermalize with finite couplings for finite times. Numerical simulations support the analytics: The system thermalizes to the NATS, rather than to the canonical prediction. Our proposal can be implemented with ultracold atoms, nitrogen-vacancy centers, trapped ions, quantum dots, and perhaps nuclear magnetic resonance. This work introduces noncommuting charges from QI-theoretic thermodynamics into quantum many-body physics: atomic, molecular, and optical physics and condensed matter.

Burnout and study engagement among medical students at Sun Yat-sen University, China

“…We also provide a unified mechanism with the lens of quantum thermalization to understand the QME and successfully apply the understanding to the presence and absence of QME regarding different initial states and different internal symmetries including SU(2) and Z 2 symmetries. For a nonintegrable system under Hamiltonian H with some conserved commuting or noncommuting charges Q a , the thermal equilibrium state is given by quantum thermodynamics as [72][73][74][75][76][77]…”

Noncommutative generalized Gibbs ensemble in isolated integrable quantum systems

“…Finally, we remark that the quantum-information-theoretic thermodynamics using noncommutative conserved quantities has attracted attention [57]. An experimental protocol for its realization has been proposed in small nonintegrable systems [58]. Our NCGGE arising in large integrable systems provides another route to the quantum-information-theoretic thermodynamics.…”

Lack of symmetry restoration after a quantum quench: An entanglement asymmetry study

“…As we will see now, the situation here is particularly subtle, due to the presence of a non-Abelian set of conserved charges for the Hamiltonian (9), a feature also known as superintegrability [42]. Non-Abelian charges also found application in other contexts such as quantum thermodynamics [43][44][45][46][47] and time crystals [48,49].…”