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.Comment: 38 pages, RevTeX v3.0, figures available upon request; Caltech
Preprint #MAP-15
We present a practical solution to the "sign problem" in the auxiliary field Monte Carlo approach to the nuclear shell model. The method is based on extrapolation from a continuous family of problem-free Hamiltonians. To demonstrate the resultant ability to treat large shell-model problems, we present results for 54 Fe in the full f p-shell basis using the Brown-Richter interaction. We find the Gamow-Teller β + strength to be quenched by 58% relative to the single-particle estimate, in better agreement with experiment than previous estimates based on truncated bases.
We present novel Monte Carlo methods for treating the interacting shell model
that allow exact calculations much larger than those heretofore possible. The
two-body interaction is linearized by an auxiliary field; Monte Carlo
evaluation of the resulting functional integral gives ground-state or thermal
expectation values of few-body operators. The ``sign problem'' generic to
quantum Monte Carlo calculations is absent in a number of cases. We discuss the
favorable scaling of these methods with nucleon numb er and basis size and
their suitability to parallel computation.Comment: 13 pages, MAP-14
We present the first auxiliary field Monte Carlo calculations for a rare earth nucleus, 170 Dy. A pairing plus quadrupole Hamiltonian is used to demonstrate the physical properties that can be studied in this region. We calculate various static observables for both uncranked and cranked systems and show how the shape distribution evolves with temperature. We also introduce a discretization of the path integral that allows a more efficient Monte Carlo sampling.
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