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The severity of the sign problem in lattice QCD at nonzero baryon density is measured by the average phase of the fermion determinant. Motivated by the equivalence of chiral random matrix theory and QCD to leading order in the epsilon…

Long-range interactions in finite density QCD necessitate a non-perturbative approach in order to reliably map out the key features and spectrum of the QCD phase diagram. However, the complex nature of the fermion determinant in this sector…

Quantum field theories at finite matter densities generically possess a partition function that is exponentially suppressed with the volume compared to that of the phase quenched analogue. The smallness arises from an almost uniform…

If the fermion mass is large enough, the phase of the fermion determinant of QCD at finite density is strongly correlated with the imaginary part of the Polyakov loop. This fact can be exploited to reduce the fluctuations of the phase…

A nonperturbative lattice study of QCD at finite chemical potential is complicated due to the complex fermion determinant and the sign problem. Here we apply the method of stochastic quantization and complex Langevin dynamics to this…

At nonzero quark chemical potential dynamical lattice simulations of QCD are hindered by the sign problem caused by the complex fermion determinant. The severity of the sign problem can be assessed by the average phase of the fermion…

The sign problem of QCD prevents standard lattice simulations to determine the phase diagram of strong interactions with a finite chemical potential directly. Complex Langevin simulations provide an alternative method to sample path…

We propose a new approach to finite density QCD based on a histogram method with phase quenched simulations at finite chemical potential. Integrating numerically the derivatives of the logarithm of the quark determinant with respect to the…

The sign problem obstructs the determination of the QCD phase diagram in the temperature-baryon chemical potential plane using lattice QCD. We review the sign problem in QCD and related field theories, including applications to real-time…

We investigate the properties of the half-filling point in lattice QCD (LQCD), in particular the disappearance of the sign problem and the emergence of an apparent particle-hole symmetry, and try to understand where these properties come…

Recently, cluster methods have been used to solve a variety of sign problems including those that arise in the presence of fermions. In all cases an analytic partial re-summation over a class of configurations in the path integral was…

We study the expectation value of the phase of the fermion determinant for Wilson lattice fermions with chemical potential. We use quenched SU(3) ensembles and implement a recently proposed exact dimensional reduction of the fermion…

The expectation value of the complex phase factor of the fermion determinant is computed in the microscopic domain of QCD at nonzero chemical potential. We find that the average phase factor is non-vanishing below a critical value of the…

The effect of the complex phase of the fermion determinant is a key question related to the sign problem in finite-density QCD. Recently it has been shown that ignoring the complex phase -- the phase quenching -- does not change physics in…

The cold and dense regime of the QCD phase diagram is to this day inaccessible to first principle lattice calculations owing to the sign problem. Here we present progress of an ongoing effort to probe this particularly difficult regime…

QCD at finite densities of heavy quarks is investigated using the density-of-states method. The phase factor expectation value of the quark determinant is calculated to unprecedented precision as a function of the chemical potential.…

Quantum Monte-Carlo (QMC) simulations involving fermions have the notorious sign problem. Some well-known exceptions of the auxiliary field QMC algorithm rely on the factorizibility of the fermion determinant. Recently, a fermionic QMC…

We show how the prescription of taking the absolute value of the fermion determinant in the integration measure of QCD at finite density, forgetting its phase, reproduces the correct thermodynamical limit. This prescription, which applies…

We study the high density region of QCD within an effective model obtained in the frame of the hopping parameter expansion and choosing Polyakov type of loops as the main dynamical variables representing the fermionic matter. To get a first…

We consider the heavy-dense limit of QCD at finite fermion density in the canonical formulation and approximate it by a 3-state Potts model. In the strong coupling limit, the model is free of the sign problem. Away from the strong coupling,…