On the Sign Problem in the Hirsch-Fye Algorithm for Impurity Problems

We show that there is no fermion sign problem in the Hirsch and Fye algorithm for the single-impurity Anderson model. Beyond the particle-hole symmetric case for which a simple proof exists, this has been known only empirically. Here we prove the nonexistence of a sign problem for the general case by showing that each spin trace for a given Ising configuration is separately positive. We further use this insight to analyze under what conditions orbitally degenerate Anderson models or the two-impurity Anderson model develop a sign.