2017/01/31 by Peng Ye, Meng Cheng, Eduardo Fradkin · 33 citations
Materials Science · Mathematics · Physics and Astronomy · #Axion #Charge (physics) #Combinatorics #Duality (order theory) #Fermion #Graphene research and applications #Mathematical physics #Mathematics #Order (exchange) #Particle physics #Physics #Quantum #Quantum many-body systems #Quantum mechanics #Topological Materials and Phenomena #Topological insulator #Topological order #Topological quantum number #Topology (electrical circuits) #Type (biology) #cond-mat.mtrl-sci #cond-mat.str-el #hep-th #math-ph #math.MP
paper · pdf · doi:10.1103/physrevb.96.085125
published in Physical review. B./Physical review. B 96(8) (American Physical Society) · 10 pages
arxiv created 2017/07/22 · openalex created_date 2017/08/17 · openalex publication_date 2017/08/18 · arxiv updated 2017/08/22 · openalex updated_date 2026/08/06
In this paper, we propose a generalization of the S-duality of four-dimensional quantum electrodynamics (QED4) to QED4 with fractionally charged excitations, the fractional S-duality. Such QED4 can be obtained by gauging the U(1) symmetry of a topologically ordered state with fractional charges. When time-reversal symmetry is imposed, the axion angle (\ensuremathθ) can take a nontrivial but still time-reversal-invariant value \ensuremathπ/t2 (t\ensuremath∈ℤ). Here, 1/t specifies the minimal electric charge carried by bulk excitations. Such states with time-reversal and U(1) global symmetry (fermion number conservation) are fractional topological insulators (FTIs). We propose a topological quantum field theory description, which microscopically justifies the fractional S-duality. Then, we consider stacking operations (i.e., a direct sum of Hamiltonians) among FTIs. We find that there are two topologically distinct classes of FTIs: type I and type II. Type I (t\ensuremath∈ℤodd) can be obtained by directly stacking a noninteracting topological insulator and a fractionalized gapped fermionic state with minimal charge 1/t and vanishing \ensuremathθ. But type II (t\ensuremath∈ℤeven) cannot be realized through any stacking. Finally, we study the surface topological order of fractional topological insulators.