Related papers: Complex saddle points and the sign problem in comp…
We suggest an approach for simulating theories with a sign problem that relies on optimisation of complex integration contours that are not restricted to lie along Lefschetz thimbles. To that end we consider the toy model of a…
We study three possible ways to circumvent the sign problem in the O(3) nonlinear sigma model in 1+1 dimensions. We compare the results of the worm algorithm to complex Langevin and multiparameter reweighting. Using the worm algorithm, the…
The sign problem at nonzero chemical potential prohibits the use of importance sampling in lattice simulations. Since complex Langevin dynamics does not rely on importance sampling, it provides a potential solution. Recently it was shown…
A simple integral relation between a complex weight and the corresponding positive distribution is derived by introducing a second complex variable. Together with the positivity and normalizability conditions, this sum rule allows to…
We investigate a simple model using the numerical simulation in the complex Langevin equation (CLE) and the analytical approximation with the Gaussian Ansatz. We find that the Gaussian Ansatz captures the essential and even quantitative…
The path optimization method, which is proposed to control the sign problem in quantum field theories with continuous degrees of freedom by machine learning, is applied to a spin model with discrete degrees of freedom. The path optimization…
We search saddle points for a large class of convex-concave Lagrangian. A generalized explicit iterative scheme based on Arrow-Hurwicz method converges to a saddle point of the problem. We also propose in this work, a convergent…
The Monte Carlo evaluation of path integrals is one of a few general purpose methods to approach strongly coupled systems. It is used in all branches of Physics, from QCD/nuclear physics to the correlated electron systems. However, many…
Effective Polyakov line models, derived from SU(3) gauge-matter systems at finite chemical potential, have a sign problem. In this article I solve two such models, derived from SU(3) gauge-Higgs and heavy quark theories by the relative…
The complex Langevin (CL) method is a classical numerical strategy to alleviate the numerical sign problem in the computation of lattice field theories. Mathematically, it is a simple numerical tool to compute a wide class of…
Towards a solution to the sign problem in the simulations of systems having indefinite or complex-valued measures, we propose a new approach which yields statistical errors smaller than the crude Monte Carlo using absolute values of the…
We consider saddle point problems which objective functions are the average of $n$ strongly convex-concave individual components. Recently, researchers exploit variance reduction methods to solve such problems and achieve linear-convergence…
To tackle the sign problem in the simulations of systems having indefinite or complex-valued measures, we propose a new approach which yields statistical errors smaller than the crude Monte Carlo using absolute values of the original…
Self-interacting scalar quantum field theories possessing $PT$-symmetry are physically admissible since their energy spectrum is real and bounded below. However, models with $PT$-invariant potentials can have complex actions in general and…
In this article, we dwell into the class of so-called ill-posed Linear Inverse Problems (LIP) which simply refers to the task of recovering the entire signal from its relatively few random linear measurements. Such problems arise in a…
We propose a novel approach toward the general solution of the sign problem in real-time path-integral simulations. Using a recursive multilevel blocking strategy, this method circumvents the sign problem by synthesizing the phase…
Monte Carlo simulation of gauge theories with a $\theta$ term is known to be extremely difficult due to the sign problem. Recently there has been major progress in solving this problem based on the idea of complexifying dynamical variables.…
The Picard-Lefschetz theory has been attracting much attention as a tool to evaluate a multi-variable integral with a complex weight, which appears in various important problems in theoretical physics. The idea is to deform the integration…
Recently, the problem of local minima in very high dimensional non-convex optimization has been challenged and the problem of saddle points has been introduced. This paper introduces a dynamic type of normalization that forces the system to…
The nuclear shell model is known to describe the properties of various nuclei extremely well. However, the auxiliary-field quantum Monte Carlo calculations cannot be applied to it with general interactions due to the sign problem. The model…