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

Understand

The sign problem is a notorious problem, which occurs in Monte Carlo simulations of a system with the partition function whose integrand is not real positive.

• The basic idea of the factorization method applied on such a system is to control some observables in order to determine and sample efficiently the region of configuration space which gives important contribution to the partition function.
• We argue that it is crucial to choose appropriately the set of the observables to be controlled in order for the method to work successfully 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.