Excitation-detector principle and the algebraic theory of planon-only abelian fracton orders

• URL: http://arxiv.org/abs/2506.21773v1
• Date: Thu, 26 Jun 2025 21:12:34 GMT
• Title: Excitation-detector principle and the algebraic theory of planon-only abelian fracton orders
• Authors: Evan Wickenden, Wilbur Shirley, Agnès Beaudry, Michael Hermele,
• Abstract summary: quadratic abelian planon-only fracton orders: a class of three-dimensional (3d) gapped quantum phases in which all excitations are abelian particles restricted to move in planes with fractional common normal direction.<n>We consider the 2d abelian anyon theory obtained by spatially compactifying a planon-only fracton order in a transverse direction.<n>A key ingredient is a structure theorem for finitely generated torsion-free modules over $mathbbZ_pk [tpm]$, where $p$ is prime and $k$ a
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study abelian planon-only fracton orders: a class of three-dimensional (3d) gapped quantum phases in which all fractional excitations are abelian particles restricted to move in planes with a common normal direction. In such systems, the mathematical data encoding fusion and statistics comprises a finitely generated module over a Laurent polynomial ring $\mathbb{Z}[t^\pm]$ equipped with a quadratic form giving the topological spin. The principle of remote detectability requires that every planon braids nontrivially with another planon. While this is a necessary condition for physical realizability, we observe - via a simple example - that it is not sufficient. This leads us to propose the $\textit{excitation-detector principle}$ as a general feature of gapped quantum matter. For planon-only fracton orders, the principle requires that every detector - defined as a string of planons extending infinitely in the normal direction - braids nontrivially with some finite excitation. We prove this additional constraint is satisfied precisely by perfect theories of excitations - those whose quadratic form induces a perfect Hermitian form. To justify the excitation-detector principle, we consider the 2d abelian anyon theory obtained by spatially compactifying a planon-only fracton order in a transverse direction. We prove the compactified 2d theory is modular if and only if the original 3d theory is perfect, showing that the excitation-detector principle gives a necessary condition for physical realizability that we conjecture is also sufficient. A key ingredient is a structure theorem for finitely generated torsion-free modules over $\mathbb{Z}_{p^k} [t^\pm]$, where $p$ is prime and $k$ a natural number. Finally, as a first step towards classifying perfect theories of excitations, we prove that every theory of prime fusion order is equivalent to decoupled layers of 2d abelian anyon theories.

Related papers

• Holographic duality from Howe duality: Chern-Simons gravity as an ensemble of code CFTs [0.0]
  We discuss the holographic correspondence between 3d "Chern-Simons gravity" and an ensemble of 2d Narain code CFTs.<n>We show that the mathematical identity underlying this holographic duality can be understood and rigorously proven.
  arXiv  Detail & Related papers  (2025-04-11T17:40:52Z)
• Bridging conformal field theory and parton approaches to SU(n)_k chiral spin liquids [48.225436651971805]
  We employ the $mathrmSU(n)_k$ Wess-Zumino-Witten (WZW) model in conformal field theory to construct lattice wave functions in both one and two dimensions.<n>The spins on all lattice sites are chosen to transform under the $mathrmSU(n)$ irreducible representation with a single row and $k$ boxes in the Young tableau.
  arXiv  Detail & Related papers  (2025-01-16T14:42:00Z)
• Geometry of degenerate quantum states, configurations of $m$-planes and invariants on complex Grassmannians [55.2480439325792]
  We show how to reduce the geometry of degenerate states to the non-abelian connection $A$. We find independent invariants associated with each triple of subspaces. Some of them generalize the Berry-Pancharatnam phase, and some do not have analogues for 1-dimensional subspaces.
  arXiv  Detail & Related papers  (2024-04-04T06:39:28Z)
• Broken Symmetry and Fractionalized Flux Strings in a Staggered U(1) Pure Gauge Theory [0.0]
  We study the case of $3D$ $mathrmU(1)$ pure gauge theory, simulating the staggered case numerically in its dual formulation. We find evidence of a continuum limit with a spontaneously broken $bbZ$ single-site symmetry, in contrast to the ordinary theory. Moreover, the confining string fractionalizes into multiple strands which separate spatial regions in distinct ground states of the broken symmetry.
  arXiv  Detail & Related papers  (2023-09-29T10:08:21Z)
• Non-Abelian braiding of graph vertices in a superconducting processor [144.97755321680464]
  Indistinguishability of particles is a fundamental principle of quantum mechanics. braiding of non-Abelian anyons causes rotations in a space of degenerate wavefunctions. We experimentally verify the fusion rules of the anyons and braid them to realize their statistics.
  arXiv  Detail & Related papers  (2022-10-19T02:28:44Z)
• Annihilating Entanglement Between Cones [77.34726150561087]
  We show that Lorentz cones are the only cones with a symmetric base for which a certain stronger version of the resilience property is satisfied. Our proof exploits the symmetries of the Lorentz cones and applies two constructions resembling protocols for entanglement distillation.
  arXiv  Detail & Related papers  (2021-10-22T15:02:39Z)
• Photon-mediated Stroboscopic Quantum Simulation of a $\mathbb{Z}_{2}$ Lattice Gauge Theory [58.720142291102135]
  Quantum simulation of lattice gauge theories (LGTs) aims at tackling non-perturbative particle and condensed matter physics. One of the current challenges is to go beyond 1+1 dimensions, where four-body (plaquette) interactions, not contained naturally in quantum simulating devices, appear. We show how to prepare the ground state and measure Wilson loops using state-of-the-art techniques in atomic physics.
  arXiv  Detail & Related papers  (2021-07-27T18:10:08Z)
• Quantum double aspects of surface code models [77.34726150561087]
  We revisit the Kitaev model for fault tolerant quantum computing on a square lattice with underlying quantum double $D(G)$ symmetry. We show how our constructions generalise to $D(H)$ models based on a finite-dimensional Hopf algebra $H$.
  arXiv  Detail & Related papers  (2021-06-25T17:03:38Z)
• $\mathbb{Z}_2$ lattice gauge theories and Kitaev's toric code: A scheme for analog quantum simulation [0.0]
  Kitaev's toric code is an exactly solvable model with $mathbbZ$-topological order. Our work paves the way for realizing non-Abelian anyons in analog quantum simulators.
  arXiv  Detail & Related papers  (2020-12-09T18:59:58Z)
• Covariant Origin of the $U(1)^3$ model for Euclidean Quantum Gravity [0.0]
  We show that the Abelian analog of the Palatini or Holst formulation is a consistent but topological theory without propagating degrees of freedom. We also derive a pure connection formulation of Euclidian GR including a cosmological constant.
  arXiv  Detail & Related papers  (2020-10-30T18:22:37Z)
• Topological Quantum Gravity of the Ricci Flow [62.997667081978825]
  We present a family of topological quantum gravity theories associated with the geometric theory of the Ricci flow. First, we use BRST quantization to construct a "primitive" topological Lifshitz-type theory for only the spatial metric. We extend the primitive theory by gauging foliation-preserving spacetime symmetries.
  arXiv  Detail & Related papers  (2020-10-29T06:15:30Z)
• In and around Abelian anyon models [6.509665408765348]
  We provide an explicit algorithm for a $K$-matrix in Chern-Simons theory and a positive definite even one for a lattice conformal field theory. Anyon models and chiral conformal field theories underlie the bulk-edge correspondence for topological phases of matter.
  arXiv  Detail & Related papers  (2020-04-25T03:39:43Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.