LOOP ALGORITHMS FOR QUANTUM SIMULATIONS OF FERMION MODELS ON LATTICES

Two cluster algorithms, based on constructing and flipping loops, are presented for world-line quantum Monte Carlo simulations of fermions a nd are tested on the one-dimensional repulsive Hubbard model. We call these algorithms the loop-flip and loop-exchange algorithms. For these two algorithms and the standard world-line algorithm, we calculated t he autocorrelation times for various physical quantities and found tha t the ordinary world-line algorithm, which uses only local moves, suff ers from very long correlation times that makes not only the estimate of the error difficult but also the estimate of the average values the mselves difficult. These difficulties are especially severe in the low -temperature, large-U regime. In contrast, we find that new algorithms , when used alone or in combinations with themselves and the standard algorithm, can have significantly smaller autocorrelation times, in so me cases being smaller by three orders of magnitude. The new algorithm s, which use nonlocal moves, are discussed from the point of view of a general prescription for developing cluster algorithms. The loop-flip algorithm is also shown to be ergodic and to belong to the grand cano nical ensemble. Extensions to other models and higher dimensions are b riefly discussed.