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Register a new userRecent developments at finite density on the lattice
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Gert Aarts
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Some recent developments to handle the numerical sign problem in QCD and related theories at nonzero density are reviewed. In this contribution I focus on changing the integration order to soften the severity of the sign problem, the density of states, and the extension into the complex plane (complex Langevin dynamics and Lefshetz thimbles).
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QCD matter at finite temperature and density is a subject that has witnessed very impressive theoretical developments in the recent years. In this review I will discuss some new insights on the microscopic degrees of freedom of the QCD medium near the chiral crossover transition from lattice QCD. Latest high precision lattice data on the fluctuations and correlations between conserved charges like the baryon number, strangeness can help us to understand and distinguish between different models of interacting hadrons. Furthermore, the latest constraints on the location of the critical end-point and the curvature of the critical line will be discussed. In the later part of this review I will discuss about the insights on the thermal nature of the medium created in heavy ion collision experiments that have come from the theoretical analysis of the particle yields, and to what extent the lattice data on correlations and fluctuations of conserved charges can give us any information about the fireball at freezeout.
A brief overview of the QCD phase diagram at nonzero temperature and density is provided. It is explained why standard lattice QCD techniques are not immediately applicable for its determination, due to the sign problem. We then discuss a selection of recent lattice approaches that attempt to evade the sign problem and classify them according to the underlying principle: constrained simulations (density of states, histograms), holomorphicity (complex Langevin, Lefschetz thimbles), partial summations (clusters, subsets, bags) and change in integration order (strong coupling, dual formulations).
The hadron resonance gas (HRG) model is often believed to correctly describe the confined phase of QCD. This assumption is the basis of many phenomenological works on QCD thermodynamics and of the analysis of hadron yields in relativistic heavy ion collisions. We use first-principle lattice simulations to calculate corrections to the ideal HRG. Namely, we determine the sub-leading fugacity expansion coefficients of the grand canonical free energy, receiving contributions from processes like kaon-kaon or baryon-baryon scattering. We achieve this goal by performing a two dimensional scan on the imaginary baryon number chemical potential ($mu_B$) - strangeness chemical potential ($mu_S$) plane, where the fugacity expansion coefficients become Fourier coefficients. We carry out a continuum limit estimation of these coefficients by performing lattice simulations with temporal extents of $N_tau=8,10,12$ using the 4stout-improved staggered action. We then use the truncated fugacity expansion to extrapolate ratios of baryon number and strangeness fluctuations and correlations to finite chemical potentials. Evaluating the fugacity expansion along the crossover line, we reproduce the trend seen in the experimental data on net-proton fluctuations by the STAR collaboration.
The QCD equation of state at finite baryon density is studied in the framework of a Cluster Expansion Model (CEM), which is based on the fugacity expansion of the net baryon density. The CEM uses the two leading Fourier coefficients, obtained from lattice simulations at imaginary $mu_B$, as the only model input and permits a closed analytic form. Excellent description of the available lattice data at both $mu_B = 0$ and at imaginary $mu_B$ is obtained. We also demonstrate how the Fourier coefficients can be reconstructed from baryon number susceptibilities.
We study the phase diagram of QCD at finite isospin density using two flavors of staggered quarks. We investigate the low temperature region of the phase diagram where we find a pion condensation phase at high chemical potential. We started a basic analysis of the spectrum at finite isospin density. In particular, we measured pion, rho and nucleon masses inside and outside of the pion condensation phase. In agreement with previous studies in two-color QCD at finite baryon density we find that the Polyakov loop does not depend on the density in the staggered formulation.
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