Monte Carlo calculations of conformal dimensions of large charge operators. Invited Physics Seminar. Indian Institute of Science. July 5, 2019
We test the recent proposal for computing conformal dimensions using a large charge expansion using Monte Carlo methods. 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 regularization” of the original model. Such simpler formulations of scalar quantum field theories have become interesting recently from the perspective of quantum computing. Here we again find that the $(j,j)$ sector continues to show excellent agreement with the predicted large charge expansion up to small values of $j$. However, preliminary results on the behavior of the next subleading sector $(j,j-1)$ suggests a less satisfying scenario.
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