Related papers: Real-Time Dynamics in Two Dimensions with Tensor N…
Advanced algorithms are necessary to obtain faster-than-real-time dynamic simulations in a number of different physical problems that are characterized by widely disparate time scales. Recent advanced dynamic Monte Carlo algorithms that…
Fractional and tempered fractional partial differential equations (PDEs) are effective models of long-range interactions, anomalous diffusion, and non-local effects. Traditional numerical methods for these problems are mesh-based, thus…
A novel class of non-reversible Markov chain Monte Carlo schemes relying on continuous-time piecewise-deterministic Markov Processes has recently emerged. In these algorithms, the state of the Markov process evolves according to a…
Thermodynamics of dissipative quantum systems with double-well potentials is studied by the path-integral Monte Carlo (PIMC) method without truncation to the two-state model. For efficient simulation at low temperatures, we develop a new…
The influence matrix (IM) provides a powerful framework for characterizing nonequilibrium quantum many-body dynamics by encoding multitime correlations into tensor-network states. Understanding how its computational complexity relates to…
Partial differential equations (PDEs) with spatially-varying coefficients arise throughout science and engineering, modeling rich heterogeneous material behavior. Yet conventional PDE solvers struggle with the immense complexity found in…
Tensor product state (TPS) based methods are powerful tools to efficiently simulate quantum many-body systems in and out of equilibrium. In particular, the one-dimensional matrix-product (MPS) formalism is by now an established tool in…
The multilevel Monte Carlo (MLMC) method has proven to be an effective variance-reduction statistical method for Uncertainty quantification in PDE models. It combines approximations at different levels of accuracy using a hierarchy of…
The venerable 2D point-vortex model plays an important role as a simplified version of many disparate physical systems, including superfluids, Bose-Einstein condensates, certain plasma configurations, and inviscid turbulence. This system is…
Neural-network quantum states (NQS) offer a versatile and expressive alternative to traditional variational ans\"atze for simulating physical systems. Energy-based frameworks, like Hopfield networks and Restricted Boltzmann Machines,…
Artificial Neural Networks were recently shown to be an efficient representation of highly-entangled many-body quantum states. In practical applications, neural-network states inherit numerical schemes used in Variational Monte Carlo, most…
We review the local Monte Carlo dynamics and Swendsen-Wang cluster algorithm. We introduce and analyze a new Monte Carlo dynamics known as transitional Monte Carlo. The transitional Monte Carlo algorithm samples energy probability…
The MPSDynamics.jl package provides an easy to use interface for performing open quantum systems simulations at zero and finite temperatures. The package has been developed with the aim of studying non-Markovian open system dynamics using…
Quantum Monte Carlo (QMC) is an advanced simulation methodology for studies of manybody quantum systems. In this review, we focus on the electronic structure QMC, i.e., methods relevant for systems described by the electron-ion…
We propose a new variational Monte Carlo (VMC) method with an energy variance extrapolation for large-scale shell-model calculations. This variational Monte Carlo is a stochastic optimization method with a projected correlated condensed…
Projected entangled-pair states (PEPS) constitute a powerful variational ansatz for capturing ground state physics of two-dimensional quantum systems. However, accurately computing and minimizing the energy expectation value remains…
Monte Carlo methods are widely used for neutron transport simulations at least partly because of the accuracy they bring to the modeling of these problems. However, the computational burden associated with the slow convergence rate of Monte…
We propose a method to study dynamical response of a quantum system by evolving it with an imaginary-time dependent Hamiltonian. The leading non-adiabatic response of the system driven to a quantum-critical point is universal and…
The Minimally Entangled Typical Thermal States (METTS) are an ensemble of pure states, equivalent to the Gibbs thermal state, that can be efficiently represented by tensor networks. In this article, we use the Projected Entangled Pair…
We study interacting Majorana fermions in two dimensions as a low-energy effective model of a vortex lattice in two-dimensional time-reversal-invariant topological superconductors. For that purpose, we implement ab-initio quantum Monte…