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SUMMARY:A 2D-CFT Factory: Critical Lattice Models Derived from generalised
  symmetries - POTTER ROOM - CMS - Ling Yan Hung (Tsinghua University)
DTSTART:20251030T130000Z
DTEND:20251030T140000Z
UID:TALK240301@talks.cam.ac.uk
DESCRIPTION:In this talk\, we introduce a ``CFT factory&rsquo\;&rsquo\; : 
 a novel algorithm of methodically generating 2D lattice models that would 
 flow to 2D conformal fixed points in the infrared. These 2D models are rea
 lised by giving critical boundary conditions to 3D TQFT \, described by st
 ring-net models\, often called the strange correlators. We engineer these 
 critical boundary conditions by harnessing the non-commutativity of genera
 tors of generalised non-invertible symmetries\, realised as anyons in the 
 3D TQFT . The non-invertible symmetries preserved at the critical point ca
 n be controlled by studying a novel ``refined condensation tree&rsquo\;&rs
 quo\;. Our structured method generates an infinite family of critical latt
 ice models\, including the A-series minimal models\, and uncovers previous
 ly unknown critical points. Notably\, we find at least three novel critica
 l points (c&asymp\;1.3\, 1.8\, and 2.5 respectively) preserving the Haager
 up symmetries\, in addition to recovering previously reported ones. The co
 ndensation tree\, together with a generalised Kramers-Wannier duality\, pr
 edicts precisely large swathes of phase boundaries\, fixes almost complete
 ly the global phase diagram\, and sieves out second order phase transition
 s. This is not only illustrated in well-known examples (such as the 8-vert
 ex model related to the A5 category) but also further verified with precis
 ion numerics\, using our improved (non-invertible) symmetry-preserving ten
 sor-network RG\, in novel examples involving the Haagerup symmetries. We s
 how that critical couplings can be precisely encoded in the categorical da
 ta (Frobenius algebras and quantum dimensions in unitary fusion categories
 )\, thus establishing a powerful\, systematic route to discovering and pot
 entially classifying new conformal field theories.
LOCATION:External
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