# Monte Carlo calculations of conformal dimensions of large charge operators. Invited Physics Seminar. Indian Institute of Science. July 5, 2019

Invited Talk

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.

### Service Performed By

- Chandrasekharan, Shailesh Professor of Physics

### Date

- July 5, 2019

### Service or Event Name

- Invited Physics Seminar

### Host Organization

- Indian Institute of Science

### Location or Venue

- Bengaluru, India