Document Type
Article
Publication Date
1-22-2021
Publication Title
Physics Reports
Abstract
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 Langevin to quantum field theory in relativistic and nonrelativistic quantum matter, with an emphasis on the nonrelativistic case.
Keywords
Complex Langevin, Sign problem, Stochastic quantization
Volume
892
First Page
1
Last Page
54
DOI
10.1016/j.physrep.2020.09.002
ISSN
03701573
Recommended Citation
Berger, Casey E.; Rammelmüller, L.; Loheac, A. C.; Ehmann, F.; Braun, J.; and Drut, J. E., "Complex Langevin and Other Approaches to the Sign Problem in Quantum Many-Body Physics" (2021). Physics: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/phy_facpubs/99
Comments
Peer reviewed accepted manuscript.