This thesis presents the path-integral formulation of the nuclear shell model using the Hubbard-Stratonovich transformation, which linearizes the two-body interaction by auxiliary fields. The path-integral was evaluated via Monte Carlo. The method scales favorably with valence-nucleon number and shell-model basis: full-basis calculations can be done up to the rare-earth region, which cannot be treated by other methods. Observables are calculated for the ground state and in a thermal ensemble. Dynamical correlations are obtained, from which strength functions are extracted through the Maximum Entropy method. Examples in the s-d shell, where exact diagonalization can be carried out, compare well with exact results. The "sign problem", which is generic to fermion Monte Carlo calculations, is proved to be absent in a wide class of interactions including the attractive pairing-plus-multipole interactions. The formulation is general for interacting fermion systems and is well suited for parallel computation. The method has been implemented on the Intel Touchstone Delta System, achieving better than 99% parallelization.This thesis presents the path-integral formulation of the nuclear shell model using the Hubbard-Stratonovich transformation, which linearizes the two-body interaction by auxiliary fields. The path-integral was evaluated via Monte Carlo. The method scales favorably with valence-nucleon number and shell-model basis: full-basis calculations can be done up to the rare-earth region, which cannot be treated by other methods. Observables are calculated for the ground state and in a thermal ensemble. Dynamical correlations are obtained, from which strength functions are extracted through the Maximum Entropy method. Examples in the s-d shell, where exact diagonalization can be carried out, compare well with exact results. The "sign problem", which is generic to fermion Monte Carlo calculations, is proved to be absent in a wide class of interactions including the attractive pairing-plus-multipole interactions. The formulation is general for interacting fermion systems and is well suited for parallel computation. The method has been implemented on the Intel Touchstone Delta System, achieving better than 99% parallelization.

Nov 18, 20090 citations

Fermion Monte Carlo algorithms and liquid He3

Robert M. Panoff, Joseph Carlson

Variational Monte Carlo and several many-fermion Green's-function Monte Carlo (GFMC) algorithms are used to study the ground state of liquid $^{3}\mathrm{He}$ . We report the first mirror potential GFMC calculations in a many-fermion problem, comparing them with transient estimation and fixed-node studies to illustrate the strengths and weaknesses of each. GFMC results with the Aziz HFDHE2 interaction are in good agreement with experiment, yielding energies within approximately 0.1 K per particle. In addition, each of these calculations predict a kinetic energy per particle of between 12 and 12.5 K.Variational Monte Carlo and several many-fermion Green's-function Monte Carlo (GFMC) algorithms are used to study the ground state of liquid $^{3}\mathrm{He}$. We report the first mirror potential GFMC calculations in a many-fermion problem, comparing them with transient estimation and fixed-node studies to illustrate the strengths and weaknesses of each. GFMC results with the Aziz HFDHE2 interaction are in good agreement with experiment, yielding energies within approximately 0.1 K per particle. In addition, each of these calculations predict a kinetic energy per particle of between 12 and 12.5 K.

Physical Review LettersMar 6, 1989121 citations

A Monte-Carlo method for fermionic many-body problems

Stefan Rombouts

Jan 1, 19973 citations

Monte Carlo procedure for 2-dimensional fermion systems

I. Morgenstern, Diethelm W�rtz

The European Physical Journal BJun 1, 19854 citations

Green’s-function Monte Carlo for lattice fermions: Application to the t−J model

C. Stephen Hellberg, Efstratios Manousakis

We develop a general numerical method to study the zero-temperature properties of strongly correlated electron models on large lattices. The technique, which resembles Green's-function Monte Carlo, projects the ground-state component from a trial wave function with no approximations. We use this method to determine the phase diagram of the two-dimensional $t\ensuremath{-}J$ model, using the Maxwell construction to investigate electronic phase separation. The shell effects of fermions on finite-sized periodic lattices are minimized by keeping the number of electrons fixed at a closed-shell configuration and varying the size of the lattice. Results obtained for various electron numbers corresponding to different closed shells indicate that the finite-size effects in our calculation are small. For any value of interaction strength, we find that there is always a value of the electron density above which the system can lower its energy by forming a two-component phase separated state. Our results are compared with other calculations on the $t\ensuremath{-}J$ model. We find that the most accurate results are consistent with phase separation at all interaction strengths.We develop a general numerical method to study the zero-temperature properties of strongly correlated electron models on large lattices. The technique, which resembles Green's-function Monte Carlo, projects the ground-state component from a trial wave function with no approximations. We use this method to determine the phase diagram of the two-dimensional $t\ensuremath{-}J$ model, using the Maxwell construction to investigate electronic phase separation. The shell effects of fermions on finite-sized periodic lattices are minimized by keeping the number of electrons fixed at a closed-shell configuration and varying the size of the lattice. Results obtained for various electron numbers corresponding to different closed shells indicate that the finite-size effects in our calculation are small. For any value of interaction strength, we find that there is always a value of the electron density above which the system can lower its energy by forming a two-component phase separated state. Our results are compared with other calculations on the $t\ensuremath{-}J$ model. We find that the most accurate results are consistent with phase separation at all interaction strengths.

arXiv:cond-mat/9911071Physical review. B, Condensed matterMay 1, 200046 citations

Variational Monte Carlo and several many-fermion Green's-function Monte Carlo (GFMC) algorithms are used to study the ground state of liquid

^{3}\mathrm{He}

. We report the first mirror potential GFMC calculations in a many-fermion problem, comparing them with transient estimation and fixed-node studies to illustrate the strengths and weaknesses of each. GFMC results with the Aziz HFDHE2 interaction are in good agreement with experiment, yielding energies within approximately 0.1 K per particle. In addition, each of these calculations predict a kinetic energy per particle of between 12 and 12.5 K.