1993/05/14 by G. H. Lang, Calvin W. Johnson, C. W. Johnson +2 · 1 citation
Mathematics · Physics and Astronomy · #Applied mathematics #Canonical ensemble #Hamiltonian (control theory) #Hybrid Monte Carlo #Markov chain Monte Carlo #Mathematical optimization #Mathematics #Monte Carlo method #Monte Carlo molecular modeling #Path integral Monte Carlo #Path integral formulation #Physics #Physics of Superconductivity and Magnetism #Quantum #Quantum Monte Carlo #Quantum and electron transport phenomena #Quantum mechanics #Statistical physics #Superconductivity in MgB2 and Alloys #nucl-th
paper · pdf · doi:10.1103/physrevc.48.1518
published as Phys.Rev.C48:1518-1545,1993 · 38 pages, RevTeX v3.0, figures available upon request; Caltech Preprint #MAP-159
arxiv created 1993/05/14 · openalex publication_date 1993/10/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We present in detail a formulation of the shell model as a path integral and Monte Carlo techniques for its evaluation. The formulation, which linearizes the two-body interaction by an auxiliary field, is quite general, both in the form of the effective ``one-body'' Hamiltonian and in the choice of ensemble. In particular, we derive formulas for the use of general (beyond monopole) pairing operators, as well as a novel extraction of the canonical (fixed-particle-number) ensemble via an activity expansion. We discuss the advantages and disadvantages of the various formulations and ensembles and give several illustrative examples. We also discuss and illustrate calculation of the imaginary-time response function and the extraction, by maximum entropy methods, of the corresponding strength function. Finally, we discuss the ``sign problem'' generic to fermion Monte Carlo calculations, and prove that a wide class of interactions are free of this limitation.