Sparse modeling for Quantum Monte-Carlo simulation

We show a new kind of applications of the sparse modeling to a traditional problem in the condensed-matter physics. In the quantum Monte-Carlo simulation, we observe a huge amount of data for investigation of the details of the low-energy behavior for interacting many-body systems. Although the real-time behavior is actually under investigation, the quantum Monte-Carlo simulation is performed on the imaginary time for restriction of the method. Thus we need a technique for analytical continuation connecting between the real and imaginary-time functions. However the analytical continuation can be problematic because the problem consists of solving the ill-conditioned equation. In the present study, by employing an adequate regularization, we solve efficiently the ill-conditioned equation in the analytical continuation. As a result, we have a novel way to perform the analytical continuation and find an intermediate representation between imaginary-time and real-frequency domains.