Green's function Monte Carlo method with exact imaginary-time propagation

Physically interpretable approximations of many-body spectral functions

The rational function approximation provides a natural and interpretable representation of response functions such as the many-body spectral functions. We apply the vector fitting (VFIT) algorithm to fit a variety of spectral functions calculated from the Holstein model of electron-phonon interactions. We show that the resulting rational functions are highly efficient in their fitting of sharp features in the spectral functions, and could provide a means to infer physically relevant information from a spectral data set. The position of the peaks in the approximated spectral function are determined by the location of poles in the complex plane. In addition, we developed a variant of VFIT that incorporates regularization to improve the quality of fits. With this procedure, we demonstrate it is possible to achieve accurate spectral function fits that vary smoothly as a function of physical conditions.

Reptation quantum Monte Carlo algorithm for lattice Hamiltonians with a directed-update scheme

We provide an extension to lattice systems of the reptation quantum Monte Carlo algorithm, originally devised for continuous Hamiltonians. For systems affected by the sign problem, a method to systematically improve upon the so-called fixed-node approximation is also proposed. The generality of the method, which also takes advantage of a canonical worm algorithm scheme to measure off-diagonal observables, makes it applicable to a vast variety of quantum systems and eases the study of their ground-state and excited-state properties. As a case study, we investigate the quantum dynamics of the one-dimensional Heisenberg model and we provide accurate estimates of the ground-state energy of the two-dimensional fermionic Hubbard model.

Quartic form of the slowly decaying imaginary distance beam propagation method

The governing equation of the slowly decaying imaginary distance beam propagation method (SD-ID-BPM) is further modified, for calculating the eigenmodes in optical fibers and waveguides. Its convergence is analyzed in detail and compared to the earlier version of SD-ID-BPM and other methods. It is demonstrated that the method described here can converge to the same desired accuracy within fewer propagation steps than the earlier version of SD-ID-BPM and other methods. Since the governing equation of the SD-ID-BPM is a partial differential equation with higher order derivatives, it might be interesting if the discretization in the transverse x-y plane is performed by applying the numerical techniques for partial differential equations with higher order derivatives.

Improved diffusion Monte Carlo for bosonic systems using time-step extrapolation “on the fly”

A diffusion Monte Carlo algorithm employing "on the fly" extrapolation with respect to the time step is implemented and demonstrated simulating realistic systems. Significant advantages are obtained when using on the fly extrapolation, leading to reduced systematic and statistical errors. The sound theoretical basis of extrapolation on the fly is discussed and compared to justifications for the a posteriori extrapolation.