Torus Berry Data Determine All-Genus Abelian Topological Orders

arXiv:2608.20330 · cond-mat.str-el, hep-th, math-ph, math.MP · Submitted 2026-08-20 · Read on arXiv

cond-mat.str-el, hep-th, math-ph, math.MP

Submitted: 2026-08-20

Updated: 2026-09-23

Terminology

• Topological Order — 15× in this paper · explained in 2 episodes
• Quantization — 11× in this paper · explained in 12 episodes
• Holonomy — 4× in this paper · explained in 2 episodes
• Hilbert Space — 3× in this paper · explained in 2 episodes
• Anyons — 1× in this paper · explained in 2 episodes
• Consistency — 1× in this paper · explained in 3 episodes
• Entanglement — 1× in this paper · explained in 4 episodes
• Robustness — 1× in this paper · explained in 5 episodes

Sources

• The Ground State Structure and Modular Transformations of Fractional Quantum Hall States on a Torus
• Modular transformation and bosonic/fermionic topological orders in Abelian fractional quantum Hall states
• A theory of 2+1D bosonic topological orders
• Modular transformations and topological orders in two dimensions
• Measuring Modular Matrices by Shearing Lattices
• Distinguish modular categories and 2+1D topological orders beyond modular data: Mapping class group of higher genus manifold
• Classification of abelian spin Chern-Simons theories
• Abelian Chern-Simons theory with toral gauge group, modular tensor categories, and group categories
• From classical theta functions to topological quantum field theory
• Classification of Extended Abelian Chern-Simons Theories
• Toral Chern-Simons TQFT via Geometric Quantization in Real Polarization
• Equivalence of toral Chern-Simons and Reshetikhin-Turaev theories

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