Entropic order parameters for the phases of QFT

Abstract

We propose entropic order parameters that capture the physics of generalized symmetries and phases in QFT's. We do it through an analysis of simple properties (additivity and Haag duality) of the net of operator algebras attached to space-time regions. We observe that different types of symmetries are associated with the breaking of these properties in regions of different non-trivial topologies. When such topologies are connected, we show that the non locally generated operators generate an Abelian symmetry group, and their commutation relations are fixed. The existence of order parameters with area law, like the Wilson loop for the confinement phase, or the 't Hooft loop for the dual Higgs phase, is shown to imply the existence of more than one possible choice of algebras for the same underlying theory. A natural entropic order parameter arises by this non-uniqueness. We display aspects of the phases of theories with generalized symmetries in terms of these entropic order parameters. In particular, the connection between constant and area laws for dual order and disorder parameters is transparent in this approach, new constraints arising from conformal symmetry are revealed, and the algebraic origin of the Dirac quantization condition (and generalizations thereof) is described. A novel tool in this approach is the entropic certainty relation satisfied by dual relative entropies associated with complementary regions, which quantitatively relates the statistics of order and disorder parameters.

66 pages + appendices

References in corpus (2)

• Generalized Global Symmetries
• Entanglement Entropy in (3+1)-d Free $U(1)$ Gauge Theory

Cited by in corpus (38)

• Non-Invertible Global Symmetries and Completeness of the Spectrum
• Entanglement asymmetry as a probe of symmetry breaking
• The Weak Gravity Conjecture: A Review
• The quantum Mpemba effects
• The anomaly that was not meant IIB
• On completeness and generalized symmetries in quantum field theory
• Generalized Symmetries of the Graviton
• Proof of the universal density of charged states in QFT
• A universal formula for the density of states with continuous symmetry
• Lattice T-duality from non-invertible symmetries in quantum spin chains
• Entanglement asymmetry and symmetry defects in boundary conformal field theory
• Variational approach to relative entropies (with application to QFT)
• A simpler probe of the quantum Mpemba effect in closed systems
• Entanglement asymmetry dynamics in random quantum circuits
• Mutual Information of Generalized Free Fields
• Holographic Tensor Networks with Bulk Gauge Symmetries
• Entropic order parameters in weakly coupled gauge theories
• Instability of Universal Terms in the Entanglement Entropy
• Snowmass White Paper: The Quest to Define QFT
• Relative entropic uncertainty relation for scalar quantum fields
• Symmetry breaking in chaotic many-body quantum systems at finite temperature
• Charges in the UV completion of neutral electrodynamics
• Non-Abelian entanglement asymmetry in random states
• Additivity, Haag duality, and non-invertible symmetries
• Entropic distinguishability of quantum fields in phase space
• Complexity in algebraic QFT
• ABJ anomaly as a U(1) symmetry and Noether's theorem
• Entanglement entropy of a Rarita-Schwinger field in a sphere
• Dynamics of entanglement fluctuations and quantum Mpemba effect in the $\nu =1$ QSSEP model
• Breaking global symmetries with locality-preserving operations
• Quench dynamics of entanglement entropy under projective charge measurements: the free fermion case
• Charge fluctuation entropy of Hawking radiation: a replica-free way to find large entropy
• Entropic order parameters and topological holography
• Entropic Order Parameters for Categorical Symmetries in 2D-CFT
• The Luttinger Count is the Homotopy not the Physical Charge: Generalized Anomalies Characterize Non-Fermi Liquids
• Uniqueness of purifications is equivalent to Haag duality
• Superselection Rules, Bosonization Duality in 1+1 Dimensions and Momentum-Space Entanglement
• Generalized symmetries and Noether's theorem in QFT