Related papers: Monte Carlo simulations on the Lefschetz thimble: …
To account for the interference effects of the Coulomb and exchange interactions of electrons a new path integral representation of the density matrix has been developed in the canonical ensemble at finite temperatures. The developed…
This article gives an introduction to the multilevel blocking (MLB) approach to both the fermion and the dynamical sign problem in path-integral Monte Carlo simulations. MLB is able to substantially relieve the sign problem in many…
We present real-time inchworm quantum Monte Carlo results for single-site dynamical mean field theory on an infinite coordination number Bethe lattice. Our numerically exact results are obtained on the L-shaped Keldysh contour and, being…
Stochastic quantization can potentially be used to simulate theories with a complex action due to a nonzero chemical potential. We study complex Langevin dynamics in the relativistic Bose gas analytically, using a mean field approximation.…
One of the most promising applications of ultracold gases in optical lattices is the possibility to use them as quantum emulators of more complex condensed matter systems. We provide benchmark calculations, based on exact quantum Monte…
This chapter is devoted to the computation of equilibrium (thermodynamic) properties of quantum systems. In particular, we will be interested in the situation where the interaction between particles is so strong that it cannot be treated as…
Ultracold atomic gases in optical lattices have proven to be a controllable, tunable and clean implementation of strongly interacting quantum many-body systems. An essential prospect for such quantum simulators is their ability to map out…
The sign problem of relativistic field theories at finite fermion chemical potential has been approached by deforming the domain of integration into complex field space. We present a method for selecting a deformed manifold of integration…
We investigate Lefschetz thimble structure of the complexified path-integration in the one-dimensional lattice massive Thirring model with finite chemical potential. The lattice model is formulated with staggered fermions and a compact…
We report recent progress in the study of a particular class of spin 1/2 XXZ model on two-dimensional lattices with frustrated diagonal and unfrustrated off-diagonal interactions. Quantum Monte Carlo simulations can be constructed without a…
We present a new quantum Monte Carlo algorithm suitable for generically complex problems, such as systems coupled to external magnetic fields or anyons in two spatial dimensions. We find that the choice of gauge plays a nontrivial role, and…
The Worldvolume Hybrid Monte Carlo (WV-HMC) method [arXiv:2012.08468] is a reliable and versatile algorithm for addressing the numerical sign problem. It resolves the ergodicity issues commonly encountered in Lefschetz thimble-based…
Monte Carlo sampling of any system may be analyzed in terms of an associated glass model -- a variant of the Random Energy Model -- with, whenever there is a sign problem, complex fields. This model has three types of phases (liquid, frozen…
This is a review of recent developments in Monte Carlo methods in the field of ultra cold gases. For bosonic atoms in an optical lattice we discuss path integral Monte Carlo simulations with worm updates and show the excellent agreement…
The tempered Lefschetz thimble method is a parallel-tempering algorithm towards solving the numerical sign problem. It uses the flow time of the gradient flow as a tempering parameter and is expected to tame both the sign and multimodal…
We propose a quantum Monte Carlo approach to solve the ground state many-body Schrodinger equation for the electronic ground state. The method combines optimization from variational Monte Carlo and propagation from auxiliary field quantum…
Dynamical mean field theory and its cluster extensions provide a very useful approach for examining phase transitions in model Hamiltonians, and, in combination with electronic structure theory, constitute powerful methods to treat strongly…
The sign problem is a notorious problem, which occurs in Monte Carlo simulations of a system with a partition function whose integrand is not positive. One way to simulate such a system is to use the factorization method where one enforces…
Reliable simulations of correlated quantum systems, including high-temperature superconductors and frustrated magnets, are increasingly desired nowadays to further understanding of essential features in such systems. Quantum Monte Carlo…
Recently, a Quantum Monte Carlo method alternative to the Path Integral Monte Carlo method was developed for the numerical solution of the N-boson problem; it is based on the stochastic evolution of classical fields. Here we apply it to…