Related papers: Path optimization method for the sign problem
Recently there has been remarkable progress in solving the sign problem, which occurs in investigating statistical systems with a complex weight. The two promising methods, the complex Langevin method and the Lefschetz thimble method, share…
Many fascinating systems suffer from a severe (complex action) sign problem preventing us from calculating them with Markov Chain Monte Carlo simulations. One promising method to alleviate the sign problem is the transformation of the…
Path integrals with complex actions are encountered for many physical systems ranging from spin- or mass-imbalanced atomic gases and graphene to quantum chromo-dynamics at finite density to the non-equilibrium evolution of quantum systems.…
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…
A solution to the sign problem is the so-called "Lefschetz thimble approach" where the domain of integration for field variables in the path integral is deformed from the real axis to a sub-manifold in the complex space. For properly chosen…
Recent progress of the complex Langevin method and the Lefschetz thimble in connection with the sign problem is reviewed. These methods rely on the complexification of the original field manifold and they allow direct simulations of…
We point out that Monte Carlo simulations of theories with severe sign problems can be profitably performed over manifolds in complex space different from the one with fixed imaginary part of the action. We describe a family of such…
The path optimization method with machine learning is applied to the one-dimensional massive lattice Thirring model, which has the sign problem caused by the fermion determinant. This study aims to investigate how the path optimization…
It is sometimes speculated that the sign problem that afflicts many quantum field theories might be reduced or even eliminated by choosing an alternative domain of integration within a complexified extension of the path integral (in the…
The path integral formulation of quantum mechanical problems including fermions is often affected by a severe numerical sign problem. We show how such a sign problem can be alleviated by a judiciously chosen constant imaginary offset to the…
We present a general technique for addressing sign problems that arise in Monte Carlo simulations of field theories. This method deforms the domain of the path integral to a manifold in complex field space that maximizes the average sign…
The concept of Lefschetz thimble decomposition is one of the most promising possible modifications of Quantum Monte Carlo (QMC) algorithms aimed at alleviating the sign problem which appears in many interesting physical situations, e.g. in…
As a solution towards the numerical sign problem, we propose a novel Hybrid Monte Carlo algorithm, in which molecular dynamics is performed on a continuum set of integration surfaces foliated by the antiholomorphic gradient flow ("the…
A general algorithm toward the solution of the fermion sign problem in finite-temperature quantum Monte Carlo simulations has been formulated for discretized fermion path integrals with nearest-neighbor interactions in the Trotter…
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…
We investigate the sign problem in 0+1 dimensional QCD at finite chemical potential by using the path optimization method. The SU(3) link variable is complexified to the SL(3,$\mathbb{C}$) link variable, and the integral path is represented…
We develop a way of improving complex Langevin dynamics motivated by the Lefschetz-thimble decomposition of integrals. In our method, arbitrary observables of an original model with multiple Lefschetz thimbles are computed by a modified…
We present the first practical Monte Carlo calculations of the recently proposed Lefschetz thimble formulation of quantum field theories. Our results provide strong evidence that the numerical sign problem that afflicts Monte Carlo…
The usual path integral formulation for scalar particles at finite density involves a sign problem, making numerical simulation impractical. We present alternative methods free of this difficulty. We apply these approaches to phi^4 theory…
Lattice Monte Carlo calculations of interacting systems on non-bipartite lattices exhibit an oscillatory imaginary phase known as the phase or sign problem, even at zero chemical potential. One method to alleviate the sign problem is to…