JAN 16 1995 | James E. Gubernatis, T-11 Janez Bonca, T-11 Mark Jarrell, Univ. of Cincinnati
The paper discusses the application of Bayesian inference to the analytic continuation of imaginary-time quantum Monte Carlo (MC) data, a method used to obtain real-frequency information. The authors, James E. Gubernatis, Janez Bonca, and Mark Jarrell, present a procedure based on R. K. Bryan's work, which involves using an entropic prior and a Gaussian likelihood function. The analytic continuation problem is ill-posed, requiring regularization to handle noisy and incomplete data. The authors highlight the importance of ensuring that the data used for continuation is consistent with the chosen methods, as initial numerical approaches often overlooked this step. They also discuss the challenges in achieving a Gaussian distribution of the data, which requires producing large amounts of data to approximate the central limit theorem. The paper includes illustrations and examples to demonstrate the effectiveness and limitations of their approach, emphasizing the need for careful statistical characterization of the data. The methods presented provide a framework for addressing the analytic continuation problem with clear assumptions and approximations, opening new opportunities for quantum simulation applications.The paper discusses the application of Bayesian inference to the analytic continuation of imaginary-time quantum Monte Carlo (MC) data, a method used to obtain real-frequency information. The authors, James E. Gubernatis, Janez Bonca, and Mark Jarrell, present a procedure based on R. K. Bryan's work, which involves using an entropic prior and a Gaussian likelihood function. The analytic continuation problem is ill-posed, requiring regularization to handle noisy and incomplete data. The authors highlight the importance of ensuring that the data used for continuation is consistent with the chosen methods, as initial numerical approaches often overlooked this step. They also discuss the challenges in achieving a Gaussian distribution of the data, which requires producing large amounts of data to approximate the central limit theorem. The paper includes illustrations and examples to demonstrate the effectiveness and limitations of their approach, emphasizing the need for careful statistical characterization of the data. The methods presented provide a framework for addressing the analytic continuation problem with clear assumptions and approximations, opening new opportunities for quantum simulation applications.