Related papers: Improved convergence of Complex Langevin simulatio…
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…
Peripheral heavy-ion collisions are expected to exhibit magnetic fields with magnitudes comparable to the QCD scale, as well as non-zero baryon densities. Whereas QCD at finite magnetic fields can be simulated directly with standard lattice…
In this paper we describe a new integration method for the groups $U(N)$ and $SU(N)$, for which we verified numerically that it is polynomially exact for $N\le 3$. The method is applied to the example of 1-dimensional QCD with a chemical…
The three-dimensional XY model is studied at finite chemical potential using complex Langevin dynamics. An adaptive stepsize algorithm is implemented to cure the problem of runaway solutions that appears when using a constant stepsize. The…
In the landscape of approaches toward the simulation of Lattice Models with complex action the Complex Langevin (CL) appears as a straightforward method with a simple, well defined setup. Its applicability, however, is controlled by certain…
We study the phase structure of QCD at finite temperature and density by numerical simulations on a lattice. The most important point for the numerical study at finite density is treatment of the sign problem. We propose a method to avoid…
A brief review is given of the sign problem in finite density lattice QCD and various attempts to overcome it. To date there is still no solution to this problem which would work for realistic QCD. The main focus then is on the deconfined…
State-of-the-art lattice QCD studies of hot and dense strongly interacting matter currently rely on extrapolation from zero or imaginary chemical potentials. The ill-posedness of numerical analytic continuation puts severe limitations on…
The study of QCD phase diagram is very interesting, but we have never understood it well. This is because we face a problem at finite density in QCD. The problem is called sign problem. It causes a decrease of the calculation accuracy. This…
I review recent developments in determining the QCD phase diagram by means of lattice simulations. Since the invention of methods to side-step the sign problem a few years ago, a number of additional variants have been proposed, and…
At nonzero chemical potential the numerical sign problem in lattice field theory limits the use of standard algorithms based on importance sampling. Complex Langevin dynamics provides a possible solution, but it has to be applied with care.…
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…
After a few remarks about the problem of extracting transport coefficients from lattice QCD calculations, I report on recent developments in applying stochastic quantization and complex Langevin dynamics to field theories with a complex…
Approaches to finite baryon density lattice QCD usually suffer from uncontrolled systematic uncertainties in addition to the well-known sign problem. We test a method - sign reweighting - that works directly at finite chemical potential and…
We demonstrate that the complex Langevin method (CLM) enables calculations in QCD at finite density in a parameter regime in which conventional methods, such as the density of states method and the Taylor expansion method, are not…
The complex Langevin method is a leading candidate for solving the so-called sign problem occurring in various physical situations. Its most vexing problem is that in some cases it produces `convergence to the wrong limit'. In the first…
Complex Langevin (CL) is a computational method to circumvent the numerical sign problem with applications in finite-density quantum chromodynamics and the real-time dynamics of quantum field theories. It has long been known that, depending…
In lattice field theory, the interactions of elementary particles can be computed via high-dimensional integrals. Markov-chain Monte Carlo (MCMC) methods based on importance sampling are normally efficient to solve most of these integrals.…
Lattice models with complex actions are important for the understanding of matter at finite densities, but not accessible by the standard Monte Carlo techniques due to the sign problem. Here we derive a new approach for avoiding the complex…
I review recent results on phase structure and equation of state of strong interaction matter from lattice QCD. Particular emphasis is given to the axes where direct simulations are possible and results are obtained with sufficient control…