Abstract
Finite density quantum field theories have evaded first principle Monte-Carlo simulations due to the notorious sign-problem. The partition function of such theories appears as the Fourier transform of the generalised density-of-states, which is the probability distribution of the imaginary part of the action. With the advent of Wang-Landau type simulation techniques and recent advances [1], the density-of-states can be calculated over many hundreds of orders of magnitude. Current research addresses the question whether the achieved precision is high enough to reliably extract the finite density partition function, which is exponentially suppressed with the volume. In my talk, I review the state-of-play for the high precision calculations of the density-of-states as well as the recent progress for obtaining reliable results from highly oscillating integrals. I will review recent progress for the Z3 quantum field theory for which results can be obtained from the simulation of the dual theory, which appears to free of a sign problem.
Highlights
The properties of strongly interacting matter has sparked many important investigations using accelerator experiments and large scale theoretical studies
Theoretical findings can be scrutinised against experiments, and, given the level of abstraction that went into model building, agreement would signal an understanding of the materials at hand
In the context of QCD at finite baryon densities, a variety of mechanisms have been proposed over the last couple of years that should describe the states of baryon matter in the intermediate temperature and density range with or without a strong magnetic field
Summary
The properties of strongly interacting matter has sparked many important investigations using accelerator experiments and large scale theoretical studies. At a finite baryon chemical potential, the QCD action acquires an imaginary part, and, standard Monte-Carlo techniques cannot be applied for the lattice simulation of QCD at finite densities This has become known as the notorious sign problem. Langevin simulations of lattice gauge theories avoid the positivity constraint of the Gibbs factor, which lies at the heart of Monte-Carlo simulations, and might be suitable for finite density simulations [9, 10] This technique regained a lot of interest when Aarts showed that stochastic quantisation can evade the sign problem at least for the relativistic Bose gas [11, 12]. It might appear that integrating the gluonic degrees of freedom before the fermion fields alleviates the sign problem This could be done e.g. in the strong coupling limit [15] leading to a description of Nuclear Physics suiting lattice simulations [16]. An overview on selected new methods solving the sign problem can be found in the recent review by Aarts [31]
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