ICTS

In order to test the recent proposal for computing conformal dimensions using a large charge expansion, we explore Monte Carlo methods to compute them. We focus on the O(2) and the O(4) Wilson-Fisher fixed points as test cases. Unfortunately, traditional Monte Carlo methods suffer from a severe signal-to-noise ratio problem in the large charge sectors. To overcome this bottleneck we use worldline formulations. In the O(2) case we show that conformal dimensions of charge $q$ operators obey a simple formula predicted by the large charge expansion. In the O(4) case, the charged sectors are labeled by the two SU(2) representations $(j_L,j_R)$. Since the traditional model continues to be difficult to explore in the large $(j_L, j_R)$ sectors, we study a drastically simplified alternate model, which we refer to as a "qubit" formulation. Such simpler formulations of quantum field theories have become interesting recently from the perspective of quantum computing. Here we find that while the $(j,j)$ sector continues to show excellent agreement with the predicted large charge expansion up to small values of $j$, the behavior of the next subleading sector $(j,j-1)$ is far from satisfying.