A general approach to the sign problem - the factorization method with multiple observables

摘要

The sign problem is a notorious problem, which occurs in Monte Carlosimulations of a system with the partition function whose integrand is not realpositive. The basic idea of the factorization method applied on such a systemis to control some observables in order to determine and sample efficiently theregion of configuration space which gives important contribution to thepartition function. We argue that it is crucial to choose appropriately the setof the observables to be controlled in order for the method to worksuccessfully in a general system. This is demonstrated by an explicit example,in which it turns out to be necessary to control more than one observables.Extrapolation to large system size is possible due to the nice scalingproperties of the factorized functions, and known results obtained by ananalytic method are shown to be consistently reproduced.