Spontaneous symmetry breaking from anyon condensation

Abstract

In a physical system undergoing a continuous quantum phase transition, spontaneous symmetry breaking occurs when certain symmetries of the Hamiltonian fail to be preserved in the ground state. In the traditional Landau theory, a symmetry group can break down to any subgroup. However, this no longer holds across a continuous phase transition driven by anyon condensation in symmetry enriched topological orders (SETOs). For a SETO described by a $G$-crossed braided extension $\mathcal{C}\subseteq {\mathcal{C}}_G^{\times }$, we show that physical considerations require that a connected étale algebra $A\in \mathcal{C}$ admit a $G$-equivariant algebra structure for symmetry to be preserved under condensation of $A$. Given any categorical action $\underline{G}\to {\underline{\mathsf{Aut}}}_{\otimes }^{\mathsf{br}}(\mathcal{C})$ such that $g(A)\cong A$ for all $g\in G$, we show there is a short exact sequence whose splittings correspond to $G$-equivariant algebra structures. The non-splitting of this sequence forces spontaneous symmetry breaking under condensation of $A$. Furthermore, we show that if symmetry is preserved, there is a canonically associated SETO of ${\mathcal{C}}_A^{\mathrm{loc}}$, and gauging this symmetry commutes with anyon condensation.

arXiv comment35 pages, comments welcome. To appear in Journal of High Energy Physics

References in corpus (29)

• Fault-tolerant quantum computation by anyons
• Classification of topological quantum matter with symmetries
• Symmetry protected topological orders and the group cohomology of their symmetry group
• Quantum Orders and Symmetric Spin Liquids
• Condensate induced transitions between topologically ordered phases
• A classification of symmetry enriched topological phases with exactly solvable models
• Classifying fractionalization: symmetry classification of gapped Z2 spin liquids in two dimensions
• Multi-interval Subfactors and Modularity of Representations in Conformal Field Theory
• Nets of Subfactors
• Anyon condensation and its applications
• Symmetry fractionalization and twist defects
• Theory of Twist Liquids: Gauging an Anyonic Symmetry
• Modular extensions of unitary braided fusion categories and 2+1D topological/SPT orders with symmetries
• Classification and Properties of Symmetry Enriched Topological Phases: A Chern-Simons approach with applications to Z2 spin liquids
• Quantized topological terms in weak-coupling gauge theories with symmetry and their connection to symmetry enriched topological phases
• Conformal Subnets and Intermediate Subfactors
• On Gauging Symmetry of Modular Categories
• Classification of 2+1D topological orders and SPT orders for bosonic and fermionic systems with on-site symmetries
• Tensor categories and endomorphisms of von Neumann algebras (with applications to Quantum Field Theory)
• Symmetry Fractionalization in Two Dimensional Topological Phases
• Anyon condensation and a generic tensor-network construction for symmetry protected topological phases
• Algebraic orbifold conformal field theories
• Conformal Orbifold Theories and Braided Crossed G-Categories
• Symmetry Enriched Phases via Pseudo Anyon Condensation
• Generalized Orbifold Construction for Conformal Nets
• Classification of Metaplectic Modular Categories
• Cyclic extensions of fusion categories via the Brauer-Picard groupoid
• Coherence for monoidal $G$-categories and braided $G$-crossed categories
• A Remark on CFT Realization of Quantum Doubles of Subfactors. Case Index < 4

Cited by in corpus (17)

• Classification of (2+1)D invertible fermionic topological phases with symmetry
• Relative Anomaly in (1+1)d Rational Conformal Field Theory
• Generalized Lieb-Schultz-Mattis theorem on bosonic symmetry protected topological phases
• Fractionalization of subsystem symmetries in two dimensions
• Two-dimensional topological order and operator algebras
• Emergent XY* transition driven by symmetry fractionalization and anyon condensation
• Galois Orbits of TQFTs: Symmetries and Unitarity
• Category of SET orders
• Gapped boundary of (4+1)d beyond-cohomology bosonic SPT phase
• String order parameters for symmetry fractionalization in an enriched toric code
• Quantum cellular automata and categorical dualities of spin chains
• Theory of topological defects and textures in two-dimensional quantum orders with spontaneous symmetry breaking
• Electric-magnetic duality and ${\mathbb{Z}}_2$ symmetry enriched Abelian lattice gauge theory
• On Induction for Twisted Representations of Conformal Nets
• Spacetime symmetry-enriched SymTFT: from LSM anomalies to modulated symmetries and beyond
• Proliferation transitions from a topological phase in $2+1$ dimensions
• Anomalies in mirror symmetry enriched topological orders