Loop algorithms for quantum simulations of fermion models on lattices
- Center for Nonlinear Studies and Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)
- Center for Simulational Physics, Department of Physics, University of Georgia, Athens, Georgia 30602 (United States) Supercomputer Computations Research Institute, Florida State University, Tallahassee, Florida 32306 (United States)
Two cluster algorithms, based on constructing and flipping loops, are presented for world-line quantum Monte Carlo simulations of fermions and 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 the autocorrelation times for various physical quantities and found that the ordinary world-line algorithm, which uses only local moves, suffers from very long correlation times that makes not only the estimate of the error difficult but also the estimate of the average values themselves difficult. These difficulties are especially severe in the low-temperature, large-[ital 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 some cases being smaller by three orders of magnitude. The new algorithms, 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 canonical ensemble. Extensions to other models and higher dimensions are briefly discussed.
- OSTI ID:
- 7295885
- Journal Information:
- Physical Review, B: Condensed Matter; (United States), Vol. 50:1; ISSN 0163-1829
- Country of Publication:
- United States
- Language:
- English
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