arXiv subjects

Nianrui Fu

Publications and source records attributed to Nianrui Fu.

3 recordsLinked to original sources

arXiv2026

Anyon Condensation In Symmetry-Enriched Topological Phases: $G$-Grading of Multifusion Categories

Although anyon condensation is a standard mechanism for relating topological orders, anyon condensation in symmetry-enriched topological (SET) phases is more intricate because the condensate must also be compatible with the global symmetry. We study symmetry-preserving anyon condensation in SET phases described by the enlarged Hu-Geer-Wu (HGW) string-net model with multifusion-category input data. We show that a $G$-preserving condensation is characterized by a compatible grading of the input multifusion category, and that this grading constructs the multifusion-category input of the child SET phase. To make this construction concrete, we consider the case where the relevant data come from a finite group extension $E$ of $G$ by $N$: an $E$-graded fusion category induces a $G$-SET input by passing to the quotient symmetry $G$, and the resulting input naturally carries a compatible $N$-grading that implements the further condensation inside the SET phase while preserving $G$. We illustrate the construction using three quantum-double examples: the trivial extension $\mathbb{Z}_2\times\mathbb{Z}_2$, the non-Abelian semidirect product $S_3$, and the nontrivial central extension $\mathbb{Z}_4$. The $\mathbb{Z}_4$ example further shows that symmetry fractionalized anyons do not obstruct symmetry-preserving condensation once the condensate is treated as a physical coherent state.

cond-mat.str-el↗

arXiv2025

Symmetry-Enriched Topological Phases and Their Gauging: A String-Net Model Realization

We present a systematic framework for constructing exactly-solvable lattice models of symmetry-enriched topological (SET) phases based on an enlarged version of the string-net model. We also gauge the global symmetries of our SET models to obtain string-net models of pure topological phases. Without invoking externally imposed onsite symmetry actions, our approach promotes the string-net model of a pure topological order, specified by an input unitary fusion category $\mathscr{F}$, to an SET model, specified by a multifusion category together with a set of isomorphisms. Two complementary construction strategies are developed in the main text: (i) promotion via outer automorphisms of $\mathscr{F}$ and (ii) promotion via the Frobenius algebras of $\mathscr{F}$. The global symmetries derived via these two strategies are intrinsic to topological phases and are thus termed blood symmetries, as opposed to adopted symmetries, which can be arbitrarily imposed on topological phases. We propose the concept of symmetry-gauging family of topological phases, which are related by gauging their blood symmetries. With our approach, we construct the first explicit lattice realization of a nonabelian-symmetry-enriched topological phase -- the $S_3$ symmetry-enriched $\mathbb{Z}_2 \times \mathbb{Z}_2$ quantum-double phase. The approach further reveals the role of local excitations in SET phases and establishes their symmetry constraints.

cond-mat.str-el↗

arXiv2025

Nonlinear Symmetry-Fragmentation of Nonabelian Anyons In Symmetry-Enriched Topological Phases: A String-Net Model Realization

Symmetry-enriched topological (SET) phases combine intrinsic topological order with global symmetries, giving rise to novel symmetry phenomena. While SET phases with Abelian anyons are relatively well understood, those involving nonabelian anyons remain elusive. This obscurity stems from the multidimensional internal gauge spaces intrinsic to nonabelian anyons -- a feature first made explicit in [1,2] and further explored and formalized in our recent works [3-8]. These internal spaces can transform in highly nontrivial ways under global symmetries. In this work, we employ an exactly solvable model -- the multifusion Hu-Geer-Wu string-net model introduced in a companion paper [9] -- to reveal how the internal gauge spaces of nonabelian anyons transform under symmetries. We uncover a universal mechanism, global symmetry fragmentation (GSF), whereby symmetry-invariant anyons exhibit internal Hilbert space decompositions into eigensubspaces labeled by generally fractional symmetry charges. Meanwhile, symmetry-permuted anyons hybridize and fragment their internal spaces in accordance with their symmetry behavior. These fragmented structures realize genuinely nonlinear symmetry representations -- to be termed coherent representations -- that transcend conventional linear and projective classifications, reflecting the categorical nature of symmetries in topological phases. Our results identify nonlinear fragmentation as a hallmark of nonabelian SETs and suggest new routes for symmetry-enabled control in topological quantum computation.

cond-mat.str-el↗