Boson-Lattice Construction for Anyon Models

TL;DR

This paper introduces a systematic Boson-Lattice construction method to generate and understand anyon models, revealing their structure, creating new models, and uncovering a duality with gravity.

Contribution

It presents a novel, visual, and intuitive framework for constructing anyon models using bosons on lattices, unifying existing models and discovering new ones.

Findings

Generates all known tabulated anyon models

Creates new, non-tabulated anyon models

Reveals a duality between anyon models and gravity

Abstract

This work is an attempt to unveil the skeleton of anyon models. I present a construction to systematically generate anyon models. The construction uses a set of elementary pieces or fundamental anyon models, which constitute the building blocks to construct 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 whole structure. Remarkably, the construction generates essentially all tabulated anyon models. Moreover, novel anyon models (non-tabulated, to my knowledge) arise. To embody the construction I develop a very physical, visual and intuitive lexicon. An anyon model corresponds to a system of bosons in a lattice. By varying the number of bosons and the number of lattice sites, towers of more and more complex anyon models are built up. It is a Boson-Lattice construction. A self-similar anatomy is revealed: an anyon model is a graph that is filled with bosons to engender a new graph that is again filled with bosons. And further, bosons curve the graph that the anyon model is: I disclose a geography in the space of anyon models, where one is born from another by deforming the geometry of space. I advance an alluring duality between anyon models and gravity.