Abstract：

In this talk, we shall introduce a CFT factory -- a novel algorithm of methodically generating 2D lattice models that would flow to conformal field theories (CFTs) in the infrared. We realise these models by engineering the boundary conditions of 3D topological orders (SymTOs) described by string-net models. The critical points are induced by a commensurate condensation of non-commuting anyons. Our structured method generates an infinite family of critical lattice models, including the A-series minimal models, and uncovers previously unknown critical points. Notably, we discover at least three novel CFTs (with central charge c around 1.3, 1.8, and 2.5) that preserves the Haagerup symmetries, in addition to recovering previously reported examples. The non-invertible symmetries preserved at these points are dictated by a novel "refined condensation tree". The condensation trees predict large swathes of phase boundaries and sieves out second order phase transitions. This predictive power is illustrated not only in well-studied examples, such as the 8-vertex model associated with the A5 category, but also in new cases involving Haagerup symmetries, validated by an improved symmetry-preserving tensor-network renormalization group method. The critical couplings are precisely encoded in algebraic data (the Frobenius algebras and quantum dimensions of unitary fusion categories), thereby establishing a powerful and systematic route to the discovery and potential classification of new CFTs.

报告人简介：

万义顿，复旦大学物理系长聘教授。华南理工大学计算机与经济学双学士(1998)、美国宾夕法尼亚大学计算机硕士(2002)、加拿大渥太华大学物理硕士(2004)、加拿大滑铁卢大学暨圆周理论物理研究所理论物理博士(2009)，于日本近畿大学、东京大学、加拿大圆周理论物理研究所做博士后，2016年加入复旦物理系，从事拓扑物态、量子信息与计算、宇宙学等领域的研究。