Abstract:
The work presents the recent developments in Quantum Monte Carlo calculations for nuclear systems including strange degrees of freedom. The Auxiliary Field Diffusion Monte Carlo algorithm has been extended to the strange sector by the inclusion of the lightest among the hyperons, the $\Lambda$ particle. This allows to perform detailed calculations for $\Lambda$ hypernuclei, providing a microscopic framework for the study of the hyperon-nucleon interaction in connection with the available experimental information. The extension of the method for strange neutron matter, put the basis for the first Diffusion Monte Carlo analysis of the hypernuclear medium, with the derivation of neutron star observables of great astrophysical interest.

Abstract:
We present an accurate numerical study of the equation of state of nuclear matter based on realistic nucleon--nucleon interactions by means of Auxiliary Field Diffusion Monte Carlo (AFDMC) calculations. The AFDMC method samples the spin and isospin degrees of freedom allowing for quantum simulations of large nucleonic systems and can provide quantitative understanding of problems in nuclear structure and astrophysics.

Abstract:
We present an accurate numerical study of the equation of state of nuclear matter based on realistic nucleon--nucleon interactions by means of Auxiliary Field Diffusion Monte Carlo (AFDMC) calculations. The AFDMC method samples the spin and isospin degrees of freedom allowing for quantum simulations of large nucleonic systems and represents an important step forward towards a quantitative understanding of problems in nuclear structure and astrophysics.

Abstract:
We explore a novel and straightforward solution to the sign problem that has plagued the Auxiliary-field Monte Carlo (AFMC) method applied to many-body systems for more than a decade. We present a solution to the sign problem that has plagued the Auxiliary-field Monte Carlo (AFMC) method for more than a decade and report a breakthrough where excellent agreement between AFMC and exact CI calculations for fully realistic nuclear applications is achieved. This result offers the capability, unmatched by other methods, to achieve exact solutions for large-scale quantum many-body systems.

Abstract:
We report on the most recent applications of the Auxiliary Field Diffusion Monte Carlo (AFDMC) method. The equation of state (EOS) for pure neutron matter in both normal and BCS phase and the superfluid gap in the low--density regime are computed, using a realistic Hamiltonian containing the Argonne AV8' plus Urbana IX three--nucleon interaction. Preliminary results for the EOS of isospin--asymmetric nuclear matter are also presented.

Abstract:
The shell-model Monte Carlo (SMMC) technique transforms the traditional nuclear shell-model problem into a path-integral over auxiliary fields. We describe below the method and its applications to four physics issues: calculations of sdpf- shell nuclei, a discussion of electron-capture rates in pf-shell nuclei, exploration of pairing correlations in unstable nuclei, and level densities in rare earth systems.

Abstract:
We apply the auxiliary-field Monte Carlo approach to the nuclear shell model in the 1s-0d configuration space. The Hamiltonian was chosen to have isovector pairing and isoscalar multipole-multipole interactions, and the calculations were performed within the fixed-particle, canonical ensemble. The results demonstrate the feasibility of the method for $N\neq Z$ even-even and odd-odd N=Z nuclei. In particular, static observables for even-even Ne isotopes and Na-22 compare well with results obtained from exact diagonalization of the Hamiltonian. Response functions are presented for Ne-22 and compared with exact results, and the viability of cranked calculations for $N\neq Z$ even-even nuclei is addressed. We present methods for computing observables in the canonical ensemble using Fourier extraction, and for determining the nuclear shape.

Abstract:
This article describes Monte-Carlo algorithms for charged systems using constrained updates for the electric field. The method is generalized to treat inhomogeneous dielectric media, electrolytes via the Poisson-Boltzmann equation and considers the problem of charge and current interpolation for off lattice models. We emphasize the differences between this algorithm and methods based on the electrostatic potential, calculated from the Poisson equation.

Abstract:
We present variational Monte Carlo calculations of the neutron matter equation of state using chiral nuclear forces. The ground-state wavefunction of neutron matter, containing non-perturbative many-body correlations, is obtained from auxiliary-field quantum Monte Carlo simulations of up to about 340 neutrons interacting on a 10^3 discretized lattice. The evolution Hamiltonian is chosen to be attractive and spin-independent in order to avoid the fermion sign problem and is constructed to best reproduce broad features of the chiral nuclear force. This is facilitated by choosing a lattice spacing of 1.5 fm, corresponding to a momentum-space cutoff of Lambda = 414 MeV/c, a resolution scale at which strongly repulsive features of nuclear two-body forces are suppressed. Differences between the evolution potential and the full chiral nuclear interaction (Entem and Machleidt Lambda = 414 MeV) are then treated perturbatively. Our results for the equation of state are compared to previous quantum Monte Carlo simulations which employed chiral two-body forces at next-to-next-to-leading order (N2LO). In addition we include the effects of three-body forces at N2LO, which provide important repulsion at densities higher than 0.02 fm^-3, as well as two-body forces at N3LO.

Abstract:
We present a continuous-time Monte Carlo method for quantum impurity models, which combines a weak-coupling expansion with an auxiliary-field decomposition. The method is considerably more efficient than Hirsch-Fye and free of time discretization errors, and is particularly useful as impurity solver in large cluster dynamical mean field theory (DMFT) calculations.