arXiv:2010.08917 · Physical review. B./Physical review. B

Fractonic order in infinite-component Chern-Simons gauge theories

Xiuqi Ma, Wilbur E. Shirley, Meng Cheng, Michael Levin, John McGreevy, Xie Chen

Published May 18, 2022• 25 citations

Abstract

The Chern-Simons theory is a powerful tool in the study of 2+1D topological phases, especially quantum Hall systems. Here, the authors extend the framework by allowing an infinite number of gauge fields and use it to study the 3+1D fracton order. Fracton order has been studied mostly using lattice models and higher-rank gauge theories. The introduction of the Chern-Simons formulation allows the user to take advantage of theoretical tools developed over the past decades for quantum Hall systems. In particular, the authors are able to study foliated fracton order more systematically and identify a new type of fracton order, not possible in previous formulations.

DOI: 10.1103/physrevb.105.195124

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arXiv:2010.08917 · Physical review. B./Physical review. B

Fractonic order in infinite-component Chern-Simons gauge theories

Xiuqi Ma, Wilbur E. Shirley, Meng Cheng, Michael Levin, John McGreevy, Xie Chen

Published May 18, 2022• 25 citations

arXiv HTML PDF

Abstract

DOI: 10.1103/physrevb.105.195124

Related papers

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A_{ij}

(symmetric tensor) with gauge transformation

\delta A_{ij} = \partial_i \partial_j \alpha

; fractonic Chern-Simons action:

S = \frac{k}{4\pi} \int \epsilon^{\mu\nu\rho} A_{\mu} \partial_\nu A_{\rho}

generalized to higher-rank; fracton charge conservation:

\partial_i \partial_j J_{ij} = 0

; dipole moment conservation:

\int x^i \rho

constant. | CONNECTION: Crystallographic group symmetries (e.g., cubic, hexagonal) constrain allowed higher-rank tensor gauge fields; lattice structures (e.g., square, triangular) yield subdimensional particle mobility; no direct golden ratio or base-60 link found. | DEPTH: 8 — Fractonic Chern-Simons theory unifies higher-rank gauge theory with topological order, revealing new quantum phase Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

F[\phi] = r\phi^2 + u\phi^4 + \cdots

, broken symmetry group

G \to H

; topological order: ground-state degeneracy

\text{GSD} \sim e^{cL}

(fractons) or

\text{GSD} \sim L^g

(toric code,

g

= genus); Chern–Simons action

S_{CS} = \frac{k}{4\pi}\int \text{Tr}(A \wedge dA + \frac{2}{3}A^3)

; fracton gauge theory:

S = \int (B_{ij}\partial_t A_{ij} - \text{...})

with symmetric tensor gauge fields

A_{ij}

. | CONNECTION: Fracton phases exhibit sub-dimensional particle motion — point excitations confined to lines or planes — mirroring the geometry of root systems and lattice symmetries (e.g., cubic lattices with

C_4

rotational symmetry); the

k

level in Chern–Simons theory is quantized (integer), linking to mo Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

\mathbb{Z}_N

gauge theories in 2D that exhibit topological order whose quasiparticles have constrained mobility and whose ground-state degeneracy shows ultraviolet (UV) dependence. These features are reminiscent of spatial symmetry-enriched topological order, wherein quasiparticle excitations transform nontrivially under lattice translations. We further propose a Chern-Simons variant that produces non-CSS stabilizer codes and outline a framework for exponentially symmetric subsystem SPT phases. Finally, we extend this gauging procedure to 3D, obtaining new variants of fracton topological order.