Related papers: Monte Carlo simulations on the Lefschetz thimble: …
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…
Determining the dynamics of interacting integrable many-particle quantum systems at finite times after homogeneous quantum quenches is a long-standing challenge. We present a Monte Carlo sampling scheme that numerically evaluates the…
Non-perturbative lattice QCD calculations at non vanishing baryon number density are hampered by the QCD sign problem. The path integral, that in lattice QCD is calculated numerically, becomes highly oscillating. One possible solution is…
We present a new approach for Monte Carlo simulations of lattice quantum spin systems which is able to eliminate the negative sign problem. Its complexity is linear in the volume of the lattice. Its efficiency is tested on a simple…
We review recent attempts at dealing with the sign problem in Monte Carlo calculations by deforming the region of integration in the path integral from real to complex fields. We discuss the theoretical foundations, the algorithmic issues…
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…
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…
Quantum Monte Carlo (QMC) methods are the gold standard for studying equilibrium properties of quantum many-body systems -- their phase transitions, ground and thermal state properties. However, in many interesting situations QMC methods…
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…
Quantum field theories (QFTs) at finite densities of matter generically involve complex actions. Standard Monte-Carlo simulations based upon importance sampling, which have been producing quantitative first principle results in particle…
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…
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…
Lefschetz thimbles regularisation of (lattice) field theories was put forward as a possible solution to the sign problem. Despite elegant and conceptually simple, it has many subtleties, a major one boiling down to a plain question: how…
A novel algorithm of Diagrammatic Quantum Monte Carlo in momentum representation is reported in details. New models can be studied with this algorithm. For Bose systems with attractive interaction, the algorithm is free of the well-known…
In this paper, by analyzing the underlying Lefschetz thimble structure, we study quantum phases in zero-dimensional scalar field theories with complex actions. Using first principles, we derive the Lefschetz thimble equations of these…
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…
Sign problem in fermion quantum Monte Carlo (QMC) simulation appears to be an extremely hard problem. Traditional lore passing around for years tells people that when there is a sign problem, the average sign in QMC simulation approaches…
A recent reformulation [1] of the problem of Coulomb gases in the presence of a dynamical dielectric medium showed that finite temperature simulations of such systems can be accomplished on the basis of completely local Hamiltonians on a…
Quantum Monte Carlo simulations provide one of the more powerful and versatile numerical approaches to condensed matter systems. However, their application to frustrated quantum spin models, in all relevant temperature regimes, is hamstrung…
We propose an efficient method to compute the so-called residual phase that appears when performing Monte Carlo calculations on a Lefschetz thimble. The method is stochastic and its cost scales linearly with the physical volume, linearly…