A study, published in PNAS  and co-authored by MQC member Michael Wolf, reveals potential physical consequences of the recently proven undecidability of the spectral gap . The paper shows the existence of two-dimensional spin-lattices that exhibit a sharp transition from purely classical behavior to an exotic topologically ordered quantum system. The exceptional feature of the constructed spin-models is that this transition is induced by a tiny change of the size of the system and that the scale at which this occurs can be tuned to any desired order of magnitude. These 'size-driven quantum phase transitions' are proven to be thermally stable and involve local interactions that might be within experimental reach.
 J.Bausch, T.S. Cubitt, A.Lucia, D.Perez-Garcia, M.M. Wolf: "Size-driven quantum phase transitions", Proc Natl Acad Sci,115(1):19-23, Jan 2018.
 T.S. Cubitt, D. Perez-Garcia, M.M. Wolf: "Undecidability of the spectral gap", Nature, 528(7581):207– 211, Dec 2015.