Mross David F, Alicea Jason, Motrunich Olexei I
Department of Physics and Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, California 91125, USA.
Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, California 91125, USA.
Phys Rev Lett. 2016 Jul 1;117(1):016802. doi: 10.1103/PhysRevLett.117.016802. Epub 2016 Jun 27.
We explicitly derive the duality between a free electronic Dirac cone and quantum electrodynamics in (2+1) dimensions (QED_{3}) with N=1 fermion flavors. The duality proceeds via an exact, nonlocal mapping from electrons to dual fermions with long-range interactions encoded by an emergent gauge field. This mapping allows us to construct parent Hamiltonians for exotic topological-insulator surface phases, derive the particle-hole-symmetric field theory of a half-filled Landau level, and nontrivially constrain QED_{3} scaling dimensions. We similarly establish duality between bosonic topological insulator surfaces and N=2 QED_{3}.
我们明确推导了具有(N = 1)费米子味的自由电子狄拉克锥与（2 + 1）维量子电动力学（(QED_3)）之间的对偶性。这种对偶性通过从电子到对偶费米子的精确、非局部映射来实现，其中长程相互作用由一个涌现的规范场编码。这种映射使我们能够为奇异拓扑绝缘体表面相构建母体哈密顿量，推导半填充朗道能级的粒子 - 空穴对称场论，并对(QED_3)的标度维数进行非平凡约束。我们同样建立了玻色子拓扑绝缘体表面与(N = 2) (QED_3)之间的对偶性。
