Topological BF Theory construction of twisted dihedral quantum double phases from spontaneous symmetry breaking

• URL: http://arxiv.org/abs/2511.19589v1
• Date: Mon, 24 Nov 2025 19:00:00 GMT
• Title: Topological BF Theory construction of twisted dihedral quantum double phases from spontaneous symmetry breaking
• Authors: Zhi-Qiang Gao, Chunxiao Liu, Joel E. Moore,
• Abstract summary: We present a systematic construction of nonabelian dihedral quantum double phases based on a continuous $O(2)$ gauge field.<n>Our proposal offers an alternative route to nonabelian topological order with promising prospects in synthetic gauge field platforms.
• Score: 7.0272997775313835
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Nonabelian topological orders host exotic anyons central to quantum computing, yet established realizations rely on case-by-case constructions that are often conceptually involved. In this work, we present a systematic construction of nonabelian dihedral quantum double phases based on a continuous $O(2)$ gauge field. We first formulate a topological $S[O(2)\times O(2)]$ BF theory, and by identifying the Wilson loops and twist operators of this theory with anyons, we show that our topological BF theory reproduces the complete anyon data, and can incorporate all Dijkgraaf--Witten twists. Building on this correspondence, we present a microscopic model with $O(2)$ lattice gauge field coupled to Ising and rotor matter whose Higgsing yields the desired dihedral quantum double phase. A perturbative renormalization group analysis further indicates a direct transition from this phase to a $U(1)$ Coulomb or chiral topological phase at a stable multicritical point with emergent $O(3)$ symmetry. Our proposal offers an alternative route to nonabelian topological order with promising prospects in synthetic gauge field platforms.

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