We investigate a reformulation of the dynamics of interacting fermion systems in terms of a stochastic extension of time-dependent Hartree-Fock equations. From a path-integral representation of the evolution operator, we show that the exact N-body state can be interpreted as a coherent average over Slater determinants evolving in a random mean-field. The imaginary time propagation is also presented and gives a similar scheme which converges to the exact ground state. In addition, the growth of statistical errors is examined to show the stability of this stochastic formulation.

As an alternative to Wigner's spin-isospin SU(4) symmetry, known to be broken in heavier nuclei, a pseudo-SU(4) symmetry is proposed which follows from the combined invariance in pseudospin and isospin. The pseudo-SU(4) scheme is tested in N, Z . 28 nuclei, and its consequences with regard to Gamow-Teller b decay are pointed out. [S0031-9007(99)08617-2]

We propose a new projector quantum Monte-Carlo method to investigate the ground state of ultracold fermionic atoms modeled by a lattice Hamiltonian with on-site interaction. The many-body state is reconstructed from Slater determinants that randomly evolve in imaginary-time according to a stochastic mean-field motion. The dynamics prohibits the crossing of the exact nodal surface and no sign problem occurs in the Monte-Carlo estimate of observables. The method is applied to calculate ground-state energies and correlation functions of the repulsive two-dimensional Hubbard model. Numerical results for the unitary Fermi gas validate simulations with nodal constraints.PACS. 03.75.Ss, 05.30.Fk, 71.10.Fd 1. Introduction. Since the experimental achievement of Fermi degeneracy [1] with an atomic vapor, a considerable attention has been attracted by the physics of dilute ultracold fermions. The ability to tune many parameters, such as temperature, density or inter-particle interactions, makes atomic Fermi gases ideal candidates to understand a wealth of phenomena relevant for physical systems ranging from nuclear matter to high-temperature superconductors. Of particular interest is the strongly interacting regime in the transition from Bardeen-Cooper-Schrieffer (BCS) superfluidity of Cooper pairs to Bose-Einstein condensation (BEC) of atomic dimers. In the crossover regime, Fermi condensates have been observed on both the BCS and the BEC sides of a magnetically controlled Feshbach resonance [2][3][4]. The unitary regime, where the scattering length diverges, is particularly studied [5-7] to investigate the universal features of the fermionic quantum many-body problem. Using several standing laser beams, ultracold atoms can also be loaded in optical lattices where they experience all the strong many-body correlations described by the Hubbard model of solid-state physics [8,9]. Optical lattice setups may allow for engineering quantum spin models [10], fractional quantum Hall effect [11], non-Abelian gauge potentials [12] or quantum information processing [13]. In this paper, we investigate a new Monte-Carlo scheme to study strongly correlated ground states of ultracold fermions interacting on a lattice. The projection onto the ground state is performed through a reformulation of the imaginary-time Schrödinger equation in terms of Slater determinants undergoing a Brownian motion driven by the Hartree-Fock Hamiltonian. Such exact stochastic extensions of the mean-field approaches have been recently proposed for boson systems [14,15]. Up to now, the fermionic counterpart uses Slater determinants whose orbitals evolve under their own mean-field, supplemented with a stochastic one-particle-one-hole excitation [16,17]. Unfortunately, the sampling generally suffers from negative weight trajectories that cause an exponential decay of the signal-tonoise ratio, which is known as the sign problem. The convergence issue of such a Monte-Carlo calculation plagued by negative "probabilities" belongs to the class of NP hard problems and a ...

A new quantum Monte Carlo approach is proposed to investigate low-lying states of nuclei within the shell model. The formalism relies on a variational symmetry-restored wave function to guide the underlying Brownian motion. Sign or phase problems that usually plague quantum Monte Carlo fermionic simulations are controlled by constraining stochastic paths through a fixed-node-like approximation. Exploratory results in the sd and pf valence spaces with realistic effective interactions are presented. They prove the ability of the scheme to yield nearly exact yrast spectroscopies for both even- and odd-mass nuclei.