We discuss finite temperature quantum Monte Carlo methods in the framework of the interacting nuclear shell model. The methods are based on a representation of the imaginary-time many-body propagator as a superposition of one-body propagators describing non-interacting fermions moving in fluctuating auxiliary fields. Fermionic Monte Carlo calculations have been limited by a ``sign'' problem. A practical solution in the nuclear case enables realistic calculations in much larger configuration spaces than can be solved by conventional methods. Good-sign interactions can be constructed for realistic estimates of certain nuclear properties. We present various applications of the methods for calculating collective properties and level densities.
We discuss finite temperature quantum Monte Carlo methods in the framework of the interacting nuclear shell model. The methods are based on a representation of the imaginary-time many-body propagator as a superposition of one-body propagators describing non-interacting fermions moving in fluctuating auxiliary fields. Fermionic Monte Carlo calculations have been limited by a ``sign'' problem. A practical solution in the nuclear case enables realistic calculations in much larger configuration spaces than can be solved by conventional methods. Good-sign interactions can be constructed for realistic estimates of certain nuclear properties. We present various applications of the methods for calculating collective properties and level densities.
We discuss finite temperature quantum Monte Carlo methods in the framework of the interacting nuclear shell model. The methods are based on a representation of the imaginary-time many-body propagator as a superposition of one-body propagators describing non-interacting fermions moving in fluctuating auxiliary fields. Fermionic Monte Carlo calculations have been limited by a "sign" problem. A practical solution in the nuclear case enables realistic calculations in much larger configuration spaces than can be solved by conventional methods. Good-sign interactions can be constructed for realistic estimates of certain nuclear properties. We present various applications of the methods for calculating collective properties and level densities.
The formalism for the auxiliary-field Monte Carlo approach to the nuclear shell model is presented. The method is based on a linearization of the two-body part of the Hamiltonian in an imaginary-time propagator using the Hubbard-Stratonovich transformation. The foundation of the method, as applied to the nuclear many-body problem, is discussed. Topics presented in detail include: (1) the density-density formulation of the method, (2) computation of the overlaps, (3) the sign of the Monte Carlo weight function, (4) techniques for performing Monte Carlo sampling, and (5) the reconstruction of response functions from an imaginary-time auto-correlation function using MaxEnt techniques. Results obtained using schematic interactions, which have no sign problem, are presented to demonstrate the feasibility of the method, while an extrapolation method for realistic Hamiltonians is presented. In addition, applications at finite temperature are outlined.
The shell model provides a powerful framework for nuclear structure calculations. The nucleons beyond an inert magic core are confined in a valence shell and interact through an effective two-body potential generally determined from the G-matrix method. However, the applicability of the shell model remains limited by the exponential growth of the many-body space with the number of valence nucleons and with the size of the one-body space. The quantum Monte Carlo (QMC) methods may thus be considered as a potentially attractive alternative to the direct diagonalization of the Hamiltonian matrix. The many-body problem is indeed reduced to a set of stochastic one-body problems describing independent particles in a fluctuating external field. Up to date, the QMC approaches of the shell model lead to the ground-state and the thermodynamic properties, but a detailed spectroscopy of nuclei is not reachable. Furthermore, they suffer from a common pathology of fermionic QMC methods, namely the sign/phase problem, which strongly contaminates the convergence of the calculation. In this context, we will present a new QMC method, providing the "yrast spectroscopy" of nuclei, and in which the sign/phase problem is managed through the constrained path approximation that is widely used in the ab initio nuclear calculations and in condensed matter physics.
The formalism for the auxiliary-field Monte Carlo approach to the nuclear shell model is presented.The method is based on a linearization of the two-body part of the Hamiltonian in an imaginary-time propagator using the Hubbard-Stratonovich transformation.The foundation of the method, as applied to the nuclear many-body problem, is discussed.Topics presented in detail include: (1) the density-density formulation of the method, (2) computation of the overlaps, (3) the sign of the Monte Carlo weight function, (4) techniques for performing Monte Carlo sampling, and ( 5) the reconstruction of response functions from an imaginary-time auto-correlation function using MaxEnt techniques.Results obtained using schematic interactions, which have no sign problem, are presented to demonstrate the feasibility of the method, while an extrapolation method for realistic Hamiltonians is presented.In addition, applications at finite temperature are outlined.
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 number and basis size and their suitability to parallel computation.
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.