Related papers: Heavy-dense QCD, sign optimization and Lefschetz t…
The numerical simulation of various field theories at non-zero chemical potential suffers from severe complex action problems. In particular, QCD at non-zero quark density can presently not be simulated for that reason. A similar complex…
Strong coupling lattice QCD in the dual representation allows to study the full $\mu$-$T$ phase diagram, due to the mildness of the finite density sign problem. Such simulations have been performed in the chiral limit, both at finite $N_t$…
The notorious sign problem severely limits the applicability of quantum Monte Carlo (QMC) simulations, as statistical errors grow exponentially with system size and inverse temperature. A recent proposal of a quantum-computing stochastic…
QCD in two dimensions is investigated using the improved fermionic lattice Hamiltonian proposed by Luo, Chen, Xu, and Jiang. We show that the improved theory leads to a significant reduction of the finite lattice spacing errors. The quark…
Lattice QCD at finite baryon chemical potential has the infamous sign problem which hinders Monte Carlo simulations. This can be remedied by a dual representation that makes the sign problem mild. In the strong coupling limit, the dual…
The Hamiltonian formulation of Lattice QCD with staggered fermions in the strong coupling limit has no sign problem at non-zero baryon density and allows for Quantum Monte Carlo simulations. We have extended this formalism to two flavors,…
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…
We perform a detailed analysis of the fermionic sign problem in a series of one dimensional integrals, that are achieved as extreme (one-site) limits of genuine physics models. Altogether we studied a Hubbard-like, a Gross-Neveu-like, a…
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…
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…
Monte Carlo studies of QCD at finite density suffer from the sign problem, which becomes easily uncontrollable as the chemical potential $\mu$ is increased even for a moderate lattice size. In this work we make an attempt to approach the…
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…
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…
We discuss the nature of the QCD phase transition in the heavy quark high-density region by considering an effective theory in which Polyakov loops are dynamical variables. The Polyakov loop is an order parameter of $Z_3$ symmetry, and the…
We present a novel strategy to strongly reduce the severity of the sign problem, using line integrals along paths of changing imaginary action. Highly oscillating regions along these paths cancel out, decreasing their contributions. As a…
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…
Due to the intrinsic complexity of the quantum many-body problem, quantum Monte Carlo algorithms and their corresponding Monte Carlo configurations can be defined in various ways. Configurations corresponding to few Feynman diagrams often…
We review the theory and applications of complex stochastic quantization to the quantum many-body problem. Along the way, we present a brief overview of a number of ideas that either ameliorate or in some cases altogether solve the sign…
The numerical sign problem has long been a major obstacle to first-principles calculations in various important fields of physics. We report that the recently proposed algorithm, tempered Lefschetz thimble method (TLTM), and its worldvolume…
We propose a new method for simulating QCD at finite density, where interesting phases such as the color superconductivity phase is conjectured to appear. The method is based on a general factorization property of distribution functions of…