The meron-cluster algorithm was previously used to extensively study the physics associated with the spontaneous breaking of a discrete symmetry. We recently discovered that a larger class of models with spontaneous breaking of continuous symmetries can also be simulated using the meron-cluster algorithm. Here we study one of these new models which belongs to the attractive Hubbard model family. In particular we study the spontaneous breaking of the U(1) fermion number symmetry in two dimensions and find clear evidence for a Kosterlitz-Thouless transition to a superconducting phase. 1.
We present a general strategy to solve the notorious fermion sign problem using cluster algorithms. The method applies to various systems in the Hubbard model family as well as to relativistic fermions. Here it is illustrated for nonrelativistic lattice fermions. A configuration of fermion world lines is decomposed into clusters that contribute independently to the fermion permutation sign. A cluster whose flip changes the sign is referred to as a meron. Configurations containing meron clusters contribute
0 to the path integral, while all other configurations contribute
1. The cluster representation describes the partition function as a gas of clusters in the zero-meron sector.