相关论文: The basics and applications of the tempered Lefsch…

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…

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…

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…

Nowadays the term 'sign problem' is used to identify two different problems. The ideas to overcome the first type of the 'sign problem' of strongly oscillating complex valued imtegrand in the Feynman path integrals comes from…

The Worldvolume Hybrid Monte Carlo method (WV-HMC method) [arXiv:2012.08468] is a reliable and versatile algorithm towards solving the sign problem. Similarly to the tempered Lefschetz thimble method, this method removes the ergodicity…

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…

The great majority of algorithms employed in the study of lattice field theory are based on Monte Carlo's importance sampling method, i.e. on probability interpretation of the Boltzmann weight. Unfortunately in many theories of interest one…

One of the main challenges in simulations on Lefschetz thimbles is the computation of the relative weights of contributing thimbles. In this paper we propose a solution to that problem by means of computing those weights using a reweighting…

Thimble regularisation of lattice field theories has been proposed as a solution to the infamous sign problem. It is conceptually very clean and powerful, but it is in practice limited by a potentially very serious issue: in general many…

For a given Markov chain Monte Carlo (MCMC) algorithm, we define the distance between configurations that quantifies the difficulty of transitions. This distance enables us to investigate MCMC algorithms in a geometrical way, and we…

The Worldvolume Hybrid Monte Carlo (WV-HMC) method [arXiv:2012.08468] is an efficient and versatile algorithm that mitigates the sign problem while resolving the ergodicity issues inherent in Lefschetz-thimble approaches. We focus on cases…

We study the heavy-dense limit of QCD on the lattice with heavy quarks at high density. The effective three dimensional theory has a sign problem which is alleviated by sign optimization where the path integration domain is deformed in…

The Landau-Lifshitz equation describes the dynamics of magnetization in ferromagnetic materials. Due to the essential nonlinearity and nonconvex constraint, it is typically solved numerically. In this paper, we developed a finite volume…

A second order accurate numerical scheme is proposed and implemented for the Landau-Lifshitz-Gilbert equation, which models magnetization dynamics in ferromagnetic materials, with large damping parameters. The main advantages of this method…

We introduce a robust numerical method for determining intersection numbers of Lefschetz thimbles in multivariable settings. Our approach employs the multiple shooting method to solve the upward flow equations from the saddle points to the…

Lefschetz thimbles and complex Langevin dynamics both provide a means to tackle the numerical sign problem prevalent in theories with a complex weight in the partition function, e.g. due to nonzero chemical potential. Here we collect some…

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…

A method is proposed to handle the sign problem in the simulation of systems having indefinite or complex-valued measures. In general, this new approach, which is based on renormalisation blocking, is shown to yield statistical errors…

We show that complex Langevin simulation converges to a wrong result, by relating it to the Lefschetz-thimble path integral, when the path-integral weight has different phases among dominant complex saddle points. Equilibrium solution of…

Monte Carlo simulations of lattice quantum field theories on Lefschetz thimbles are non trivial. We discuss a new Monte Carlo algorithm based on the idea of computing contributions to the functional integral which come from complete flow…