Boson-lattice construction for anyon models

Paredes, Belen (2019): Boson-lattice construction for anyon models. In: Physical Review B, Bd. 99, Nr. 20, 205154

Abstract

Can we find a physical intuitive language to represent the complex mathematical properties of anyon models? Is there a hidden organization in the space of anyon models? Can we systematically construct complex anyon models from other, more simple, anyon models? This work is an attempt to understand and explore the anatomy of the space of anyon models. I develop a construction to systematically generate and interconnect anyon models. The construction is formulated in a very physical, visual, and intuitive manner. The complex mathematical properties of anyon models, usually expressed in the complex language of braided modular tensor categories, are described here using familiar simple physical concepts like bosons in lattices, Fock states, and tunneling Hamiltonians. The construction formalism is conceptually simple and appealing. As in a Lego construction, a set of building block anyon models are assembled to construct towers of other, more complex, anyon models. A principle of assembly is established that dictates how to articulate the building blocks, setting out the global blueprint for the constructed anyon model. By assembling sets of the simple Abelian Z(n) anyon models, the construction succeeds in generating towers of well known nontrivial anyon models. Moreover, novel anyon models (nontabulated, to my knowledge) arise. Furthermore, by applying the construction principle to other building blocks, such as Ising or Fibonacci, further series of anyon models are generated. In an intriguing connection, the boson-lattice construction unveils an alluring duality between anyon models and curved space geometries. Bosons induce curvature in the lattice geometry. I disclose a geography in the space of anyon models, where one is engendered from another by deforming the geometry of space. Moreover, the potential of the boson-lattice construction can be further explored via the quantum simulation of the corresponding boson-lattice systems in the versatile accessible playground of atomic systems.

• Dokumententyp: Zeitschriftenartikel
• Fakultät: Physik
• Themengebiete: 500 Naturwissenschaften und Mathematik > 530 Physik
• ISSN: 2469-9950
• Sprache: Englisch