Non-Abelian Gauged Fracton Matter Field Theory: New Sigma Models, Superfluids and Vortices

Abstract

By gauging a higher-moment polynomial degree global symmetry and a discrete charge conjugation (i.e., particle-hole) symmetry coupled to matter fields (two symmetries mutually non-commutative), we derive a new class of higher-rank tensor non-abelian gauge field theory with dynamically gauged fractonic matter fields: Non-abelian gauged fractons interact with a hybrid class of higher-rank (symmetric or generic non-symmetric) tensor gauge theory and anti-symmetric tensor topological field theory, generalizing [arXiv:1909.13879, 1911.01804]. We also apply a quantum phase transition similar to that between insulator v.s. superfluid/superconductivity (U(1) symmetry disordered phase described by a topological gauge theory or a disordered Sigma model v.s. U(1) global/gauge symmetry-breaking ordered phase described by a Sigma model with a U(1) target space underlying Goldstone modes): We can regard our tensor gauge theories as disordered phases, and we transient to their new ordered phases by deriving new Sigma models in continuum field theories. While one low energy theory is captured by degrees of freedom of rotor or scalar modes, another side of low energy theory has vortices and superfluids -- we explore non-abelian vortices (two types of vortices mutually interacting non-commutatively beyond an ordinary group structure) and their Cauchy-Riemann relation.

28 pages. Sequel to: arXiv:1909.13879, arXiv:1911.01804. Dedicated to the 70 year anniversary of Ginzburg-Landau theory [Zh. Ekaper. Teoret. Fiz. 20, 1064 (1950)] in 2020. Accepted by Physical Review Research

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Cited by in corpus (16)

• Volume-preserving diffeomorphism as nonabelian higher-rank gauge symmetry
• Non-Abelian Hybrid Fracton Orders
• Fractonic superfluids. (II). Condensing subdimensional particles
• Higher-Rank Tensor Non-Abelian Field Theory: Higher-Moment or Subdimensional Polynomial Global Symmetry, Algebraic Variety, Noether's Theorem, and Gauging
• Fracton physics of spatially extended excitations. II. Polynomial ground state degeneracy of exactly solvable models
• Covariant fracton gauge theory with boundary
• Fracton Self-Statistics
• Renormalization group analysis on emergence of higher rank symmetry and higher moment conservation
• Covariant Interacting Fractons
• Hall-like behaviour of higher rank Chern-Simons theory of fractons
• Bridging three-dimensional coupled-wire models and cellular topological states: Solvable models for topological and fracton orders
• Strings as Hyper-Fractons
• Non-Abelian fracton order from gauging a mixture of subsystem and global symmetries
• Fractonic superfluids. III. Hybridizing higher moments
• Infinite-component $BF$ field theory: Connection of fracton order, Toeplitz braiding, and non-Hermitian amplification
• Preparing Code States via Seed-Entangler-Enriched Sequential Quantum Circuits: Application to Tetra-Digit Topological Error-Correcting Codes