ABSTRACT:
The solution to the fermion sign problem forces one to sum over a class of fermion configurations before a Monte Carlo algorithm can be designed. Conventionally this makes it necessary to compute the determinant of an N x N matrix at every step where N is large. Thus, it is important to optimize the value of N. Conventional approaches based on the Hubbard Stratanovich transformation set N = Volume or N = number of particles. We suggest a new approach in which N is optimized by the nature of the interactions. Effectively, the coupling is used to isolate a set of fermion degrees of freedom that interfere with each other and thus create a fermion bag. Thus, N is determined by the size of this bag. Using a simple example of the massless Lattice Thirring model we show that at both weak and strong couplings the bag size can be small. Thus, we can design algorithms that are far more efficient than the conventional algorithms in these regions of the coupling. |