Theory of (2+1)-dimensional fermionic topological orders and fermionic/bosonic topological orders with symmetries

Article

关键词: QUANTUM HALL STATES;    OPERATOR PRODUCT ALGEBRA;    RESONATING-VALENCE-BOND;    CHIRAL SPIN STATES;    MODULAR TRANSFORMATIONS;    EDGE EXCITATIONS;    FIELD THEORY;    CLASSIFICATION;    DEGENERACY;   

DOI  :  10.1103/PhysRevB.94.155113

来源: SCIE

【 摘 要 】

We propose a systematic framework to classify (2+1)-dimensional (2+1D) fermionic topological orders without symmetry and 2+1D fermionic/bosonic topological orders with symmetry G. The key is to use the so-called symmetric fusion category epsilon to describe the symmetry. Here, epsilon = sRep(Z(2)(f)) describing particles in a fermionic product state without symmetry, or epsilon = sRep(G(f)) [epsilon = Rep(G)] describing particles in a fermionic (bosonic) product state with symmetry G. Then, topological orders with symmetry epsilon are classified by nondegenerate unitary braided fusion categories over epsilon, plus their modular extensions and total chiral central charges. This allows us to obtain a list that contains all 2+1D fermionic topological orders without symmetry. For example, we find that, up to p + i p fermionic topological orders, there are only four fermionic topological orders with one nontrivial topological excitation: (1) the K = [GRAPHICS] fractional quantum Hall state, (2) a Fibonacci bosonic topological order stacking with a fermionic product state, (3) the time-reversal conjugate of the previous one, and (4) a fermionic topological order with chiral central charge c = 1/4, whose only topological excitation has non-Abelian statistics with spin s = 1/4 and quantum dimension d = 1 + root 2.

【 授权许可】

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