How universal is the relation between sign problem and phase transition

Abstract

The mystery of the infamous sign problem in quantum Monte Carlo simulations mightily restricts applications of the method in fermionic and frustrated systems. A recent work [Science 375, 418 (2022)] made a remarkable breakthrough in the sign problem and suggested a positive connection between the sign and phase transition. How general this argument is can be crucial in various fields related to many-body systems, such as condensed matter physics, quantum chemistry, and nuclear physics. Based on universal analyses of typical examples and numerical simulations from different approaches, we discuss when and how studying the sign can provide helpful information on phase transitions in general systems independent of specific models and algorithms. While our results support that the notorious sign offers new angles in exploring quantum many-body problems, we also notice that taking advantage of the sign can even be as challenging as neutralizing the sign problem itself in unknown systems.