Quantum Matter Theory

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Welcome to Belén Paredes group: Quantum Matter Theory!



Unveiling the skeleton of anyon models

Unveiling the skeleton of anyon models

Belén Paredes has developed a construction to systematically generate anyon models. Her construction uses a set of elementary pieces or fundamental anyon models, which constitute the building blocks to construct other, more complex, anyon models. To embody the construction she has developed a very physical, visual and intuitive lexicon. An anyon model corresponds to a system of bosons in a lattice. Her construction reveals a self-similar anatomy for anyon models: an anyon model is a graph that is filled with bosons to engender a new graph that is again filled with bosons. Moreover, she discloses a geography in the space of anyon models, where one is born from another by deforming the geometry of space. Her work advances an alluring duality between anyon models and gravity.

In this article Belén Paredes condenses the key essential ideas and results of her Boson-Lattice construction for anyon models, advancing the interesting pathways it opens up. Her work is an attempt to apprehend the subjacent texture of anyon models and thereby the anatomy of topological orders.

In this article Belén Paredes presents the full theory of her Boson-Lattice construction, carrying out a complete analysis with thorough proofs. Her mathematical results are presented in a very clear and transparent manner, using an intuitive physical language, all combined with enlightening illustrations and discussions. 
This article is best viewed in a two-page setting.