Topological Band Theory for Non-Hermitian Hamiltonians

We develop the topological band theory for systems described by non-Hermitian Hamiltonians, whose energy spectra are generally complex. After generalizing the notion of gapped band structures to the non-Hermitian case, we classify "gapped" bands in one and two dimensions by explicitly finding their topological invariants. We find nontrivial generalizations of the Chern number in two dimensions, and a new classification in one dimension, whose topology is determined by the energy dispersion rather than the energy eigenstates. We then study the bulk-edge correspondence and the topological phase transition in two dimensions. Different from the Hermitian case, the transition generically involves an extended intermediate phase with complex-energy band degeneracies at isolated "exceptional points" in momentum space. We also systematically classify all types of band degeneracies.Comment: 6 pages, 3 figures + 6 pages of supplemental materia

Integral Reduction by Unitarity Method for Two-loop Amplitudes: A Case Study

In this paper, we generalize the unitarity method to two-loop diagrams and use it to discuss the integral bases of reduction. To test out method, we focus on the four-point double-box diagram as well as its related daughter diagrams, i.e., the double-triangle diagram and the triangle-box diagram. For later two kinds of diagrams, we have given complete analytical results in general (4-2\eps)-dimension.Comment: 52 pages, 1 figur

Free boson representation of DYℏ(sl^(M+1∣N+1))DY_{\hbar}(\hat{sl} (M+1|N+1)) at level one

We construct a realization of the central extension of super-Yangian double $DY_{\hbar}(\hat{sl}(M+1|N+1))$ at level-one in terms of free boson fields with a continuous parameter.Comment: 9 pages, latex, reference revise

Non-Abelian Generalizations of the Hofstadter model: Spin-orbit-coupled Butterfly Pairs

The Hofstadter model, well-known for its fractal butterfly spectrum, describes two-dimensional electrons under a perpendicular magnetic field, which gives rise to the integer quantum hall effect. Inspired by the real-space building blocks of non-Abelian gauge fields from a recent experiment [Science, 365, 1021 (2019)], we introduce and theoretically study two non-Abelian generalizations of the Hofstadter model. Each model describes two pairs of Hofstadter butterflies that are spin-orbit coupled. In contrast to the original Hofstadter model that can be equivalently studied in the Landau and symmetric gauges, the corresponding non-Abelian generalizations exhibit distinct spectra due to the non-commutativity of the gauge fields. We derive the genuine (necessary and sufficient) non-Abelian condition for the two models from the commutativity of their arbitrary loop operators. At zero energy, the models are gapless and host Weyl and Dirac points protected by internal and crystalline symmetries. Double (8-fold), triple (12-fold), and quadrupole (16-fold) Dirac points also emerge, especially under equal hopping phases of the non-Abelian potentials. At other fillings, the gapped phases of the models give rise to $\mathbb{Z}_2$ topological insulators. We conclude by discussing possible schemes for the experimental realizations of the models in photonic platforms

Signatures of Self-Interacting Dark Matter in the Matter Power Spectrum and the CMB

We consider a self-interacting dark matter model in which the massive dark photon mediating the self-interaction decays to light dark fermions to avoid over-closing the universe. We find that if the model is constrained to explain the dark matter halos inferred for spiral galaxies and galaxy clusters simultaneously, there is a strong indication that dark matter is produced asymmetrically in the early universe. It also implies the presence of dark radiation, late kinetic decoupling for dark matter, and a suppressed linear power spectrum due to dark acoustic damping. The Lyman-$\alpha$ forest power spectrum measurements put a strong upper limit on the damping scale and the model has little room to reduce the abundances of satellite galaxies. Future observations in the matter power spectrum and the CMB, in tandem with the impact of self-interactions in galactic halos, makes it possible to measure the gauge coupling and masses of the dark sector particles even when signals in conventional dark matter searches are absent.Comment: 5 pages, 7 figures, published version in PL