Ettore Vitali

Imaginary time correlations and the phaseless auxiliary field quantum Monte Carlo

The phaseless Auxiliary Field Quantum Monte Carlo (AFQMC) method provides a well established approximation scheme for accurate calculations of ground state energies of many-fermions systems. Here we address the possibility of calculating imaginary time correlation functions with the phaseless AFQMC. We give a detailed description of the technique and test the quality of the results for static properties and imaginary time correlation functions against exact values for small systems.

Computation of dynamical correlation functions for many-fermion systems with auxiliary-field quantum Monte Carlo

We address the calculation of dynamical correlation functions for many fermion systems at zero temperature, using the auxiliary-field quantum Monte Carlo method. The two-dimensional Hubbard hamiltonian is used as a model system. Although most of the calculations performed here are for cases where the sign problem is absent, the discussions are kept general for applications to physical problems when the sign problem does arise. We study the use of twisted boundary conditions to improve the extrapolation of the results to the thermodynamic limit. A strategy is proposed to drastically reduce finite size effects relying on a minimization among the twist angles. This approach is demonstrated by computing the charge gap at half-filling. We obtain accurate results showing the scaling of the gap with the interaction strength

Imaginary time density-density correlations for two-dimensional electron gases at high density

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Equation of state of two-dimensional3He at zero temperature

, connecting to the scaling of the unrestricted Hartree-Fock method at small

Dynamical structure factor of one-dimensional hard rods

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Statistical and computational intelligence approach to analytic continuation in Quantum Monte Carlo

and Bethe Ansatz exact result in one dimension at large

Visualizing the BEC-BCS crossover in a two-dimensional Fermi gas: Pairing gaps and dynamical response functions from ab initio computations

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Linear Response of One-Dimensional Liquid ^4\hbox {He} to External Perturbations

. A new algorithm is then proposed to compute dynamical Green functions and correlation functions which explicitly varies the number of particles during the random walks in the manifold of Slater determinants. In dilute systems, such as ultracold Fermi gases, this algorithm enables calculations with much more favorable complexity, with computational cost proportional to basis size or the number of lattice sites.

Low-density phases ofHe3monolayers adsorbed on graphite

We evaluate imaginary time density-density correlation functions for two-dimensional homogeneous electron gases of up to 42 particles in the continuum using the phaseless auxiliary field quantum Monte Carlo method. We use periodic boundary conditions and up to 300 plane waves as basis set elements. We show that such methodology, once equipped with suitable numerical stabilization techniques necessary to deal with exponentials, products, and inversions of large matrices, gives access to the calculation of imaginary time correlation functions for medium-sized systems. We discuss the numerical stabilization techniques and the computational complexity of the methodology and we present the limitations related to the size of the systems on a quantitative basis. We perform the inverse Laplace transform of the obtained density-density correlation functions, assessing the ability of the phaseless auxiliary field quantum Monte Carlo method to evaluate dynamical properties of medium-sized homogeneous fermion systems.

Review of Probability Theory

We have performed a Quantum Monte Carlo study of a two-dimensional bulk sample of interacting 1/2-spin structureless fermions, a model of