Quantum Monte Carlo: What can random numbers tell us about correlated quantum systems?

摘要

Over the past decades, quantum Monte Carlo methods have proven to be very valuable for the study of quantum-mechanical many-body systems. The basic ingredient of theses methods is a decomposition of the imaginary-time evolution operator into path integrals. These paths can then be sampled using Monte Carlo techniques. Though very successful for bosons, these methods often have troubles in dealing with fermions: the fermionic antisymmetry leads to a 'sign problem'. One approach, the auxiliary-field method, has yielded slightly better results in dealing with the sign problem. Some recent developments on this method are highlighted. As a case study, it is applied to a pairing model for Fe nuclei, where indications are found for a phase transition related to nucleon-nucleon pairing. [References: 45]