Search

© 2019 American Physical Society E. E. and G. M. are partially supported by INFN through the project Quantum information technologies in Madrid (QUANTUM). S. P. K. acknowledges the support of STFC Grant No. ST/L000369/1. A. B. acknowledges support from RYC-2016-20066, FIS2015-70856-P, and CAM regional research consortium QUITEMAD+. A. B. thanks T. Byrnes for kindly sharing the document of his PhD thesis [50], A. Celi, P. Silvi, and P. Zoller for interesting discussions, and A. Celi for bringing the work [25] to our attention., The interplay of symmetry, topology, and many-body effects in the classification of phases of matter poses a formidable challenge in condensed-matter physics. Such many-body effects are typically induced by inter-particle interactions involving an action at a distance, such as the Coulomb interaction between electrons in a symmetry-protected topological (SPT) phase. In this work, we show that similar phenomena also occur in certain relativistic theories with interactions mediated by gauge bosons, and constrained by gauge symmetry. In particular, we introduce a variant of the Schwinger model or quantum electrodynamics (QED) in 1 + 1 dimensions on an interval, which displays dynamical edge states localized on the boundary. We show that the system hosts SPT phases with a dynamical contribution to the vacuum theta-angle from edge states, leading to a new type of topological QED in 1 + 1 dimensions. The resulting system displays an SPT phase which can be viewed as a correlated version of the Su-Schrieffer-Heeger topological insulator for polyacetylene due to nonzero gauge couplings. We use bosonization and density-matrix renormalization group techniques to reveal the detailed phase diagram, which can further be explored in experiments of ultra-cold atoms in optical lattices., Ministerio de Economía y Competitividad (MINECO)/FEDER, Comunidad de Madrid, INFN, Science and Technology Facilities Council (STFC), Programa Ramón y Cajal, Depto. de Física Teórica, Fac. de Ciencias Físicas, TRUE, pub

We find a large class of quantum gauge models with massless fermions where the coupling to the gauge fields is not chirally symmetric and which nevertheless do not suffer from gauge anomalies. To be specific we study two dimensional Abelian models in the Hamiltonian framework which can be constructed and solved by standard techniques. The general model describes Np photon fields and NF flavors of Dirac fermions with 2N(F)N(P) different coupling constants, i.e., the chiral component of each fermion can he coupled to the gauge fields differently We construct these models and find conditions so that no gauge anomaly appears. If these conditions hold it is possible to construct and solve the model explicitly, so that gauge- and Lorentz invariance are manifest., QC 20100525