Quantum critical points and the sign problem

Solving quantum many-body problems exposes the challenges that numerical simulations in classical computers face in exploring quantum matter. One of these is presented by the "sign problem" (SP), a fundamental limitation to investigating strongly correlated materials in condensed matter physics, solving quantum chromodynamics at finite baryon density, and computational nuclear matter studies, for example. In short, widely employed importance sampling techniques, when extended to the quantum realm, often lead to "negative probabilities" that hamper the simulations' abilities to extract convergent values of relevant physical observables. It is usually argued that the SP is not intrinsic to the physics of particular Hamiltonians since the details of how it onsets and its eventual occurrence can be altered by the choice of algorithm or many-particle basis. Despite that, I will discuss in this talk that the SP in determinant quantum Monte Carlo is linked quantitatively to quantum critical behavior. This demonstration is done via simulations of several fundamental models of condensed matter physics whose critical properties are relatively well understood. The generalization to transitions and phases, which are yet under debate, will also be discussed, including that of polarized superfluidity. I will argue that utilizing reweighting methods, the key point refers to the analytical behavior of a reference system's partition function upon change of a driving parameter in the transition, which can be tuned via different fermionic decoupling transformations or basis representations.