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

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 analyze under what conditions orbitally degenerate Anderson models or the two-impurity Anderson model develop a sign.

2 pages, no figure; published version

References in corpus (4)

• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• The Loop Algorithm
• Mesoscopic Kondo Problem
• Cluster Algorithms for Quantum Impurity Models and Mesoscopic Kondo Physics

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