Physics Commons^™

Complex Langevin And Other Approaches To The Sign Problem In Quantum Many-Body Physics, Casey E. Berger, L. Rammelmüller, A. C. Loheac, F. Ehmann, J. Braun, J. E. Drut

Physics: Faculty Publications

We review the theory and applications of complex stochastic quantization to the quantum many-body problem. Along the way, we present a brief overview of a number of ideas that either ameliorate or in some cases altogether solve the sign problem, including the classic reweighting method, alternative Hubbard–Stratonovich transformations, dual variables (for bosons and fermions), Majorana fermions, density-of-states methods, imaginary asymmetry approaches, and Lefschetz thimbles. We discuss some aspects of the mathematical underpinnings of conventional stochastic quantization, provide a few pedagogical examples, and summarize open challenges and practical solutions for the complex case. Finally, we review the recent applications of complex …