Related papers: Solving quantum impurity problems on the L-shaped …
We explore two complementary modifications of the hybridization-expansion continuous-time Monte Carlo method, aiming at large multi-orbital quantum impurity problems. One idea is to compute the imaginary-time propagation using a matrix…
The paper is the second part of the work devoted to the problem of time in quantum cosmology. Here we consider in detail two approaches within the scope of Feynman path integration scheme: The first, by Simeone and collaborators, is…
We present a numerical method for the study of correlated quantum impurity problems out of equilibrium, which is particularly suited to address steady state properties within Dynamical Mean Field Theory. The approach, recently introduced in…
The cavity method is a well established technique for solving classical spin models on sparse random graphs (mean-field models with finite connectivity). Laumann et al. [arXiv:0706.4391] proposed recently an extension of this method to…
We have developed a numerically exact approach to compute real-time path integral expressions for quantum transport problems out of equilibrium. The scheme is based on a deterministic iterative summation of the path integral (ISPI) for the…
Embedding calculations that find approximate solutions to the Schr\"{o}dinger equation for large molecules and realistic solids are performed commonly in a three step procedure involving (i) construction of a model system with effective…
We introduce real-time density matrix embedding theory (DMET), a dynamical quantum embedding theory for computing non-equilibrium electron dynamics in strongly correlated systems. As in the previously developed static DMET, real-time DMET…
We consider the numerical approximation of a generalized fractional Oldroyd-B fluid problem involving two Riemann-Liouville fractional derivatives in time. We establish regularity results for the exact solution which play an important role…
Impurities are ubiquitous in condensed matter. Boundary Conformal Field Theory (BCFT) provides a powerful method to study a localized quantum impurity interacting with a gapless continuum of excitations. The results can also be implied to…
Path integrals are a central tool when it comes to describing quantum or thermal fluctuations of particles or fields. Their success dates back to Feynman who showed how to use them within the framework of quantum mechanics. Since then, path…
We review a systematic many-body method capable of describing Fermi liquid and Non-Fermi liquid behavior of quantum impurity models at low temperatures on the same footing. The crossover to the high temperature local moment regime is…
The growing demand for solving large-scale, data-intensive linear and conic optimization problems, particularly in applications such as artificial intelligence and machine learning, has highlighted the limitations of classical interior…
In the present paper, we present an efficient continuous-time quantum Monte Carlo impurity solver with high acceptance rate at low temperature for multi-orbital quantum impurity models with general interaction. In this hybridization…
In this paper, we are concerned with the numerical solution for the backward fractional Feynman-Kac equation with non-smooth initial data. Here we first provide the regularity estimate of the solution. And then we use the backward Euler and…
This paper is concerned with numerical solutions of time-fractional nonlinear parabolic problems by a class of $L1$-Galerkin finite element methods. The analysis of $L1$ methods for time-fractional nonlinear problems is limited mainly due…
A Luttinger Liquid coupled to a quantum impurity describes a large number of physical systems. The Hamiltonian consists of left- and right-moving fermions interacting among themselves via a density-density coupling and scattering off a…
In this paper, a fully discrete local discontinuous Galerkin (LDG) finite element method is considered for solving the time-fractional KdV-Burgers-Kuramoto (KBK) equation. The scheme is based on a finite difference method in time and local…
A path integral Monte Carlo method (PIMC) based on Feynman-Kac formula for mixed boundary conditions of elliptic equations is proposed to solve the forward problem of electrical impedance tomography (EIT) on the boundary to obtain…
A numerical method is proposed for computing time-periodic and relative time-periodic solutions in dissipative wave systems. In such solutions, the temporal period, and possibly other additional internal parameters such as the propagation…
Dynamical mean-field theory (DMFT) is a useful tool to analyze models of strongly correlated fermions like the Hubbard model. In DMFT, the lattice of the model is replaced by a single impurity site embedded in an effective bath. The…