Entropic order parameters for the phases of QFT

TL;DR

This paper introduces entropic order parameters based on algebraic properties to characterize phases and symmetries in quantum field theories, providing new insights into confinement, duality, and topological aspects.

Contribution

It develops a novel entropic framework for analyzing phases of QFTs with generalized symmetries, linking algebraic properties to physical order parameters and dualities.

Findings

Entropic order parameters capture symmetry breaking and phases in QFT.

Connection between area laws and algebraic non-uniqueness of operator algebras.

Entropic certainty relations relate order and disorder parameters quantitatively.

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.