Related papers: Tempered transitions between thimbles
One strategy for reducing the sign problem in finite-density field theories is to deform the path integral contour from real to complex fields. If the deformed manifold is the appropriate combination of Lefschetz thimbles -- or somewhat…
We consider a hybrid Monte Carlo algorithm which is applicable to lattice theories defined on Lefschetz thimbles. In the algorithm, any point (field configuration) on a thimble is parametrized uniquely by the flow-direction and the…
Direct numerical evaluation of the real-time path integral has a well-known sign problem that makes convergence exponentially slow. One promising remedy is to use Picard-Lefschetz theory to flow the domain of the field variables into the…
The QCD at finite density is not well understood yet, where standard Monte Carlo simulation suffers from the sign problem. In order to overcome the sign problem, the method of Lefschetz thimble has been explored. Basically, the original…
In these proceedings, we summarize the Lefschetz thimble approach to the sign problem of Quantum Field Theories. In particular, we review its motivations, and we summarize the results of the application of two different algorithms to two…
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…
Quantum tunneling is mostly discussed in the Euclidean path integral formalism using instantons. On the other hand, it is difficult to understand quantum tunneling based on the real-time path integral due to its oscillatory nature, which…
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…
The method of tempered transitions was proposed by Neal (1996) for tackling the difficulties arising when using Markov chain Monte Carlo to sample from multimodal distributions. In common with methods such as simulated tempering and…
The simulated tempering (ST) is an important method to deal with systems whose phase spaces are hard to sample ergodically. However, it uses accepting probabilities weights which often demand involving and time consuming calculations. Here…
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…
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…
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…
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…
Lefschetz thimbles have been proposed recently as a possible solution to the complex action problem (sign problem) in Monte Carlo simulations. Here we discuss pure abelian gauge theory with a complex coupling $\beta$ and apply the concept…
The quantum Monte Carlo method on asymptotic Lefschetz thimbles is a numerical algorithm devised specifically for alleviation of the sign problem appearing in the simulations of quantum many-body systems. In this method, the sign problem is…
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…
We consider the one-dimensional massive Thirring model formulated on the lattice with staggered fermions and an auxiliary compact vector (link) field, which is exactly solvable and shows a phase transition with increasing the chemical…
In finite-size scaling analyses of Monte Carlo simulations of second-order phase transitions one often needs an extended temperature range around the critical point. By combining the parallel tempering algorithm with cluster updates and an…
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…