Solution to sign problems in half-filled spin-polarized electronic systems

We solve the sign problem in a particle-hole symmetric spin-polarized fermion model on bipartite lattices using the idea of fermion bags. The solution can be extended to a class of models at half filling but without particle-hole symmetry. Attractive Hubbard models with an odd number of fermion species can also be solved. Our solutions should allow us to study quantum phase transitions that have remained unexplored so far due to sign problems.

Figure 1

In a sample of $10000$ randomly generated configurations $[b,s,t]$ on an $8\times 8$ square lattice at $\beta =10$ involving the matrices of size $250\times 250$, we obtained 4972 positive determinants and 5028 negative determinants. A histogram of positive determinants (left) and negative determinants (right) in this sample is plotted above. The similarity of the two distributions suggests the existence of a severe sign problem.