Projects per year
Abstract
We continue our work on lattice models of webs, which generalise the wellknown loop models to allow for various kinds of bifurcations [1,2]. Here we define new web models corresponding to each of the ranktwo spiders considered by Kuperberg [3]. These models are based on the A_{2}, G_{2} and B_{2} Lie algebras, and their local vertex configurations are intertwiners of the corresponding qdeformed quantum algebras. In all three cases we define a corresponding model on the hexagonal lattice, and in the case of B_{2} also on the square lattice. For specific rootofunity choices of q, we show the equivalence to a number of three and fourstate spin models on the dual lattice. The main result of this paper is to exhibit integrable manifolds in the parameter spaces of each web model. For q on the unit circle, these models are critical and we characterise the corresponding conformal field theories via numerical diagonalisation of the transfer matrix. In the A_{2} case we find two integrable regimes. The first one contains a dense and a dilute phase, for which we have analytic control via a Coulomb gas construction, while the second one is more elusive and likely conceals noncompact physics. Three particular points correspond to a threestate spin model with plaquette interactions, of which the one in the second regime appears to present a new universality class. In the G_{2} case we identify four regimes numerically. The B_{2} case is too unwieldy to be studied numerically in the general case, but it found analytically to contain a simpler submodel based on generators of the dilute BirmanMurakamiWenzl algebra.
Original language  English 

Article number  116530 
Pages (fromto)  154 
Number of pages  54 
Journal  NUCLEAR PHYSICS B 
Volume  1002 
DOIs  
Publication status  Published  May 2024 
MoE publication type  A1 Journal articlerefereed 
Fingerprint
Dive into the research topics of 'Integrability of ranktwo web models'. Together they form a unique fingerprint.Projects
 1 Finished

Peltola Eveliina ATpalkka: Satunnaisgeometrian konformiinvarianssi
Peltola, E. (Principal investigator), Abuzaid, O. (Project Member) & Brummet, L. (Project Member)
01/09/2021 → 31/07/2024
Project: Academy of Finland: Other research funding