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We present a study of spin-unpolarized and spin-polarized two-dimensional uniform electron liquids using variational and diffusion quantum Monte Carlo (VMC and DMC) methods with Slater-Jastrow-backflow trial wave functions. Ground-state VMC…

In this article we provide a manifestly gauge-invariant approach to charged particles. It involves (1) Green functions of gauge-invariant operators and (2) Feynman rules which do not depend on any kind of gauge-fixing condition. First, we…

A Hydrogen atom immersed in a finite jellium sphere is solved using variational quantum Monte Carlo (VQMC). The same system is also solved using density functional theory (DFT), in both the local spin density (LSDA) and self-interaction…

Normalizing Flows (NF) are powerful generative models with increasing applications in augmenting Monte Carlo algorithms due to their high flexibility and expressiveness. In this work we explore the integration of NF in Diagrammatic Monte…

Dirac-delta distributions are often crucial components of the solid-fluid coupling operators in immersed solution methods for fluid-structure interaction (FSI) problems. This is certainly so for methods like the Immersed Boundary Method…

We develop and apply the Diagrammatic Monte Carlo technique to address the problem of stability of the Dirac liquid state (in a graphene type system) against strong long-range part of the Coulomb interaction. So far, all attempts to deal…

We present extensive new \emph{ab initio} path integral Monte Carlo (PIMC) simulations of the uniform electron gas (UEG) in the high-temperature regime, $8\leq\theta=k_\textnormal{B}T/E_\textnormal{F}\leq128$. This allows us to study the…

We report the quantum phase diagram of a one-dimensional Coulomb wire obtained using the path integral Monte Carlo (PIMC) method. The exact knowledge of the nodal points of this system permits us to find the energy in an exact way, solving…

We calculate the ground-state properties of unpolarized two-component Fermi gas by the diffusion quantum Monte Carlo (DMC) methods. Using an extrapolation to the zero effective range of the attractive two-particle interaction, we find…

The uniform electron gas placed between two reservoirs is used as a model system for molecular junctions under an external bias. The energetics of the electron gas are calculated by generalizing the Thomas-Fermi-Dirac (TFD) model to…

We use a variational Monte Carlo algorithm to solve the electronic structure of two-dimensional semiconductor quantum dots in external magnetic field. We present accurate many-body wave functions for the system in various magnetic field…

For important classes of many-fermion problems, quantum Monte Carlo (QMC) methods allow exact calculations of ground-state and finite-temperature properties, without the sign problem. The list spans condensed matter, nuclear physics, and…

We propose a unifying theory for both the integral and fractional quantum Hall regimes. This theory reconciles the Finkelstein approach to localization and interaction effects with the topological issues of an instanton vacuum and…

We provide a spin-adapted formulation of the Full Configuration Interaction Quantum Monte Carlo (FCIQMC) algorithm, based on the Graphical Unitary Group Approach (GUGA), which enables the exploitation of SU(2) symmetry within this…

In this article we present an analytic solution of the famous problem of diffraction and interference of electrons through one and two slits (for simplicity, only the one-dimensional case is considered). In addition to exact formulas, we…

A wide range of disordered materials, including disordered correlated systems, show "Universal Dielectric Response" (UDR), followed by a superlinear power-law increase in their optical responses over exceptionally broad frequency regimes.…

The efficiency of the variational perturbation theory [Phys. Rev. C {\bf 62}, 045503 (2000)] formulated recently for many-particle systems is examined by calculating the ground state correlation energy of the 3D electron gas with the…

We present a generalization of the variational principle that is compatible with any Hamiltonian eigenstate that can be specified uniquely by a list of properties. This variational principle appears to be compatible with a wide range of…

This lecture is a tutorial introduction to coherent effects in disordered electronic systems. Avoiding technicalities as most as possible, I present some personal points of view to describe well-known signatures of phase coherence like weak…

Diagrammatic Monte Carlo methods provide robust routines for accurate computations of correlated electronic systems in the thermodynamical limit. Recently, its versatility was extended to SU(N) Hubbard model, where the core is a novel…