Hall-like behaviour of higher rank Chern-Simons theory of fractons

Abstract

Fracton phases of matter constitute an interesting point of contact between condensed matter and high-energy physics. The limited mobility property of fracton quasiparticles finds applications in many different contexts, including quantum information, spin liquids, elasticity, hydrodynamics, gravity and holography. In this paper we adopt a field theoretical approach to investigate the three dimensional action of a rank-2 symmetric tensor field invariant under the covariant fracton symmetry. The theory appears as a non-topological higher rank generalization of the ordinary Chern-Simons model, depending only on the traceless part of the tensor gauge field. After defining a field strength, a rank-2 traceless ``electric'' field and a ``magnetic'' vector field are identified, in analogy with the standard Chern-Simons ones. Once matter is introduced, a Hall-like behaviour with fractonic features emerges. In particular, our model shows a Hall-like dipole current, together with a vectorial ``flux-attachment'' relation for dipoles. This gives a possible starting point for a fracton - vortex duality. A gauge-fixing term is then introduced, from which propagators are computed and the counting of the degrees of freedom is performed. Finally, the energy-momentum tensor is shown to be conserved and the integrated energy density is proved to be zero, which reminds the topological nature of the standard Chern-Simons model.

31 pages, appendix and references added, version to appear on JHEP

References in corpus (28)

• Local stabilizer codes in three dimensions without string logical operators
• Fracton Phases of Matter
• Fracton hydrodynamics
• Exotic Symmetries, Duality, and Fractons in 2+1-Dimensional Quantum Field Theory
• Exotic $U(1)$ Symmetries, Duality, and Fractons in 3+1-Dimensional Quantum Field Theory
• Higher-Spin Witten Effect and Two-Dimensional Fracton Phases
• Gapless Bosonic Excitation without symmetry breaking: Novel Algebraic Spin liquid with soft Gravitons
• Foliated Quantum Field Theory of Fracton Order
• Exotic ${\mathbb{Z}}_N$ Symmetries, Duality, and Fractons in 3+1-Dimensional Quantum Field Theory
• Volume-preserving diffeomorphism as nonabelian higher-rank gauge symmetry
• Hydrodynamics of dipole-conserving fluids
• Effective Fractonic Behavior in a Two-Dimensional Exactly Solvable Spin Liquid
• Maxwell theory of fractons
• The theory of symmetric tensor field: from fractons to gravitons and back
• Gauging fractons and linearized gravity
• Massive gravity and Fierz-Pauli theory
• On the introduction of a boundary in topological field theories
• A Chern-Simons theory for dipole symmetry
• Fierz-Pauli theory reloaded: from a theory of a symmetric tensor field to linearized massive gravity
• Covariant fracton gauge theory with boundary
• A note on Harmonic Gauge(s) in Massive Gravity
• Fracton gravity from spacetime dipole symmetry
• The dimensional reduction of linearized spin-2 theories invariant under transverse diffeomorphisms
• From Chern-Simons to Tomonaga-Luttinger
• Anyon condensation web and multipartite entanglement in 2D modulated gauge theories
• Topological BF description of 2D accelerated chiral edge modes
• Holographic Projection of Electromagnetic Maxwell Theory
• Fracton-elasticity duality on curved manifolds

Cited by in corpus (6)

• Quasi-topological fractons: a 3D dipolar gauge theory
• Fractonic self-duality and covariant magnetic fractons
• Quasi-topological mass generation for 3D linearized gravity
• Covariant field theory of 3D massive fractons
• Covariant Fractons and Weitzenböck Torsion
• Edge physics and the Casimir interaction in Maxwell-Chern-Simons theory on a strip