Disorder Operators and their Descendants

Abstract

I review the concept of a {\em disorder operator}, introduced originally by Kadanoff in the context of the two-dimensional Ising model. Disorder operators acquire an expectation value in the disordered phase of the classical spin system. This concept has had applications and implications to many areas of physics ranging from quantum spin chains to gauge theories to topological phases of matter. In this paper I describe the role that disorder operators play in our understanding of ordered, disordered and topological phases of matter. The role of disorder operators, and their generalizations, and their connection with dualities in different systems, as well as with Majorana fermions and parafermions, is discussed in detail. Their role in recent fermion-boson and boson-boson dualities is briefly discussed.

39 pages, 3 figures, 137 references. New expanded version. The new manuscript has an expanded introduction, a new section 7 on dualities (including particle-vortex dualities) and their relation with the concept of disorder operators. To appear in a special memorial issue for Leo Kadanoff of the Journal of Statistical Physics

References in corpus (6)

• Non-Abelian Anyons and Topological Quantum Computation
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Quantum Spin Liquids
• A Duality Web in 2+1 Dimensions and Condensed Matter Physics
• Exotic non-Abelian anyons from conventional fractional quantum Hall states
• Parafermionic conformal field theory on the lattice

Cited by in corpus (37)

• Generalized Symmetries in Condensed Matter
• Continuous symmetries and approximate quantum error correction
• Dynamical criticality and domain-wall coupling in long-range Hamiltonians
• Higher-form symmetry breaking at Ising transitions
• Fermion disorder operator at Gross-Neveu and deconfined quantum criticalities
• Scaling of disorder operator at $(2+1)d$ U(1) quantum criticality
• Higher-Form Subsystem Symmetry Breaking: Subdimensional Criticality and Fracton Phase Transitions
• Coherent error threshold for surface codes from Majorana delocalization
• Topological Disorder Parameter
• Entanglement order parameters and critical behavior for topological phase transitions and beyond
• Constraints on order and disorder parameters in quantum spin chains
• Disorder Operator and Rényi Entanglement Entropy of Symmetric Mass Generation
• Surface codes, quantum circuits, and entanglement phases
• Characterization of topological phase transitions from a non-Abelian topological state and its Galois conjugate through condensation and confinement order parameters
• Theory of oblique topological insulators
• Universal entanglement and correlation measure in two-dimensional conformal field theories
• Topological phase transiton of anisotropic XY model with Dzyaloshinskii-Moriya interaction
• Detecting Quantum Anomalies in Open Systems
• Distinguishing Quantum Phases through Cusps in Full Counting Statistics
• Higgs Condensates are Symmetry-Protected Topological Phases: II. $U(1)$ Gauge Theory and Superconductors
• Entanglement Rényi Entropies from Ballistic Fluctuation Theory: the free fermionic case
• Probing the Topology of Fermionic Gaussian Mixed States with {U(1)} symmetry by Full Counting Statistics
• Additivity, Haag duality, and non-invertible symmetries
• Topological Defects in Quantum Field Theory with Matrix Product States
• Measuring the Boundary Gapless State and Criticality via Disorder Operator
• Topological dualities via tensor networks
• 2-Form U(1) Spin Liquids: Classical Model and Quantum Aspects
• Continuous topological phase transition between ${\mathbb{Z}}_2$ topologically ordered phases
• Quantum Computing with sine-Gordon Qubits
• Finite Correlation Length Scaling of Disorder Parameter at Quantum Criticality
• Bridging Rokhsar-Kivelson Type and Generic Quantum Phase Transitions via Thermofield Double States
• Addressing general measurements in quantum Monte Carlo
• Fundamental role of nonlocal orders in 1D Extended Bose-Hubbard Model
• Spin chains, defects, and quantum wires for the quantum-double edge
• Form Factors of the Tricritical Three-state Potts Model in its Scaling Limit
• Defects via Factorization Algebras
• Intertwined order of generalized global symmetries