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.
Highlights
AND OVERVIEW OF PREVIOUS WORKSFracton order concerns conservation laws imposed on the energetic excitations of quantum systems which have significant restrictions on their mobility:(1) Excitations cannot move without creating additional excitations.(2) Excitations can only move in certain subdimensional or subsystem directions.The origins of such constraints are conservation laws from conserved quantities of higher moments, including dipole moments [2], quadrupole moments, generalized multipole moments
Fracton order concerns conservation laws imposed on the energetic excitations of quantum systems which have significant restrictions on their mobility: (1) Excitations cannot move without creating additional excitations
The important ingredient in our present work is that the gauge structure can be noncommutative, while still coupling to the matter fields; a partial goal of our present work is to derive a non-Abelian tensor gauged fracton field theory
Summary
Fracton order (see a recent review [1] in condensed matter) concerns conservation laws imposed on the energetic excitations (such that the particle excitations are known as fractons) of quantum systems which have significant restrictions on their mobility:. (2) A pure Abelian or non-Abelian higher-rank tensor gauge theory (without coupling to gauged matter field): The Abelian case is widely studied in various works in condensed matter literature; see Refs. A rank-2 non-Abelian higher-rank tensor gauge theory with a continuous gauge structure is proposed in Ref. The most general form of rank-m non-Abelian higher-rank tensor gauge theory is given by a schematic path integral in Ref. In Sec II, we provide a systematic framework for non-Abelian gauged fractonic matter field theories. (2) An alternative type of sigma model: We formulate an alternative type of sigma model that can move between the ordered and disordered phases of these higher-rank non-Abelian tensor field theories with fully gauged fractonic matter..
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