Non-Abelian symmetry can increase entanglement entropy

Abstract

The pillars of quantum theory include entanglement and operators' failure to commute. The Page curve quantifies the bipartite entanglement of a many-body system in a random pure state. This entanglement is known to decrease if one constrains extensive observables that commute with each other (Abelian ``charges''). Non-Abelian charges, which fail to commute with each other, are of current interest in quantum thermodynamics. For example, noncommuting charges were shown to reduce entropy-production rates and may enhance finite-size deviations from eigenstate thermalization. Bridging quantum thermodynamics to many-body physics, we quantify the effects of charges' noncommutation -- of a symmetry's non-Abelian nature -- on Page curves. First, we construct two models that are closely analogous but differ in whether their charges commute. We show analytically and numerically that the noncommuting-charge case has more entanglement. Hence charges' noncommutation can promote entanglement.

4.5 pages (2 figures) + appendices (12 pages)

References in corpus (8)

• Random Quantum Circuits
• Lyapunov Exponent and Out-of-Time-Ordered Correlator's Growth Rate in a Chaotic System
• Choreographed entangle dances: topological states of quantum matter
• Entanglement Entropy of Eigenstates of Quantum Chaotic Hamiltonians
• Spin-resolved entanglement spectroscopy of critical spin chains and Luttinger liquids
• Symmetry-resolved Page curves
• Symmetry-resolved entanglement entropy in Wess-Zumino-Witten models
• Measurements in QFT: Weakly coupled local particle detectors and entanglement harvesting

Cited by in corpus (38)

• Lack of symmetry restoration after a quantum quench: an entanglement asymmetry study
• Non-Abelian eigenstate thermalization hypothesis
• Critical phase and spin sharpening in SU(2)-symmetric monitored quantum circuits
• Noncommuting conserved charges in quantum thermodynamics and beyond
• Roadmap on Quantum Thermodynamics
• Classification of dynamical Lie algebras for translation-invariant 2-local spin systems in one dimension
• Non-Abelian transport distinguishes three usually equivalent notions of entropy production
• Entanglement Entropy of ($2+1$)-Dimensional SU(2) Lattice Gauge Theory on Plaquette Chains
• Symmetry enforced entanglement in maximally mixed states
• Eigenstate thermalization hypothesis in two-dimensional XXZ model with or without SU(2) symmetry
• Estimation of Hamiltonian parameters from thermal states
• Deep thermalization under charge-conserving quantum dynamics
• Average pure-state entanglement entropy in spin systems with SU(2) symmetry
• Highly entangled stationary states from strong symmetries
• Thermalization and dephasing in collisional reservoirs
• Randomized measurement protocols for lattice gauge theories
• Designs from Local Random Quantum Circuits with SU(d) Symmetry
• Theory of Quantum Circuits with Abelian Symmetries
• Non-abelian symmetry-resolved entanglement entropy
• Symmetry breaking in chaotic many-body quantum systems at finite temperature
• Enhanced entanglement in multi-bath spin-boson models
• Noncommuting charges can remove non-stationary quantum many-body dynamics
• Eigenstate thermalization in spin-$\frac{1}{2}$ systems with SU(2) symmetry
• A Compendious Review of Majorization-Based Resource Theories: Quantum Information and Quantum Thermodynamics
• Long-time equilibration can determine transient thermality
• Imperfect Many-Body Localization in Exchange-Disordered Isotropic Spin Chains
• Subsystem Trace-Distances of Two Random States
• The Page curve from the entanglement membrane
• Automated detection of symmetry-protected subspaces in quantum simulations
• Entanglement patterns of quantum chaotic Hamiltonians with a scalar U(1) charge
• Anomalous flow in correlated quantum systems: No-go result and multiple-charge scenario
• SU(d)-Symmetric Random Unitaries: Quantum Scrambling, Error Correction, and Machine Learning
• Numerical evidence for the non-Abelian eigenstate thermalization hypothesis
• Deterministic photonic entanglement arising from non-Abelian quantum holonomy
• Thermodynamic Constraints on Information Transmission in Quantum Ensembles
• Operator entanglement in $\mathrm{SU}(2)$-symmetric dissipative quantum many-body dynamics
• Average mutual information for random fermionic Gaussian quantum states
• Constrained free energy minimization for the design of thermal states and stabilizer thermodynamic systems