Complex Paths Around The Sign Problem

Understand

The Monte Carlo evaluation of path integrals is one of a few general purpose methods to approach strongly coupled systems.

• It is used in all branches of Physics, from QCD/nuclear physics to the correlated electron systems.
• However, many systems of great importance (dense matter inside neutron stars, the repulsive Hubbard model away from half-filling, dynamical and non-equilibrium observables) are not amenable to the Monte Carlo method as it currently stands due to the so-called "sign-problem".
• We review a new set of ideas recently developed to tackle the sign problem based on the complexification of field space and the Picard-Lefshetz theory accompanying it.