Yoo, J; Chandrasekharan, S; Kaul, RK; Ullmo, D; Baranger, HU, *On the sign problem in the Hirsch-Fye algorithm for impurity problems*,
Journal of Physics A: Mathematical and General, vol. 38 no. 48
(2005),
pp. 10307-10310 [pdf], [doi] .
**Abstract:**

*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 analyse under what conditions orbitally degenerate Anderson models or the two-impurity Anderson model develop a sign. © 2005 IOP Publishing Ltd.*