Numerical simulations of correlated quantum matter: from models to field theories

 The  interpretation  of phases and  quantum phase transitions that   are  realized in nature and in model  calculations    very often hinge on   field   theories.  In this  talk,  I will concentrate on various phases of heavy fermion systems — magnetic  impurities embedded in  metallic  environments —  and  show  how  they  relate to  Higgs  condensates and  de-confined   phases.   If time  allows,  I will  furthermore  touch on exotic  phase transitions in Dirac systems.