From Sign Problems to Conformal Dimensions

The inability to solve many strongly interacting systems of interest from  first principles calculations has to do with generic features encountered  by Markov Chain Monte Carlo methods: the infamous sign problem. In the first part I show a way to solve a sign problem for the O(2)-model at finite density. Extending our methods further, we compute the anomalous dimensions of operators with arbitrary global charges in the same  model. The  calculation verified the prediction from an effective theory which computed the same quantities in a large charge expansion. We  conclude with some new directions to push the numerical studies of CFTs with global O(N) symmetry in d=3. These new models, following  the so-called *Qubit* or *D-theory* formulation are ideal candidates to realize in quantum simulators.