Deconfined Criticality in three dimensional loop models

P. Serna, M. Ortuño, A.M. Somoza, A. Nahum and J.T. Chalker

Three-dimensional loop models arise in many quantum problems, and in particular  in  quantum 
systems with SU(n) magnets. We consider a class of three-dimensional loop models where the system 
is driven across a phase transition between a phase with extended loops,
related to the Neel state, and a phase with only short loops where some symmetries of the 
lattice are broken, related to a Valence Bond Solid. 
In this phase transition we find that the system shows the features of the deconfined criticality 
scenario: there is an emergent U(1) phase with short loops and the estimates of the anomalous 
dimensions are very large for the two order parameters,
characterizing the two phases.
Notably, the built-in isotropy of the loop model implies a dynamical 
exponent equal to unity. 
We find compatible results with a continuous transition, but with peculiar and strange features.