TY - JOUR
T1 - Monte Carlo evaluation of path integrals for the nuclear shell model
AU - Lang, G. H.
AU - Johnson, C. W.
AU - Koonin, S. E.
AU - Ormand, W. E.
PY - 1993
Y1 - 1993
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=0000908129&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0000908129&partnerID=8YFLogxK
U2 - 10.1103/PhysRevC.48.1518
DO - 10.1103/PhysRevC.48.1518
M3 - Article
AN - SCOPUS:0000908129
VL - 48
SP - 1518
EP - 1545
JO - Physical Review C - Nuclear Physics
JF - Physical Review C - Nuclear Physics
SN - 0556-2813
IS - 4
ER -