### Conveners

#### Non-zero Density: QCD at Non-zero Density I

- Christof Gattringer (Austrian Science Fund FWF and University of Graz, Austria)

#### Non-zero Density: QCD at Non-zero Density II

- Christian Schmidt (Bielefeld University)

#### Non-zero Density: QCD at Non-zero Density III

- Chris Allton (Swansea University)

#### Non-zero Density: QCD at Non-zero Density IV

- Attila Pasztor (Eotvos University, Budapest)

The Bielefeld Parma collaboration has recently put forward a method to investigate the QCD phase diagram based on the computation of Taylor series coefficients at both zero and imaginary values of the baryonic chemical potential. The method is based on the computation of multi-point Padè approximants. We review the methodological aspects of the computation and, in order to gain confidence in...

We report updated results on the determination of Lee-Yang edge (LYE) singularities in $N_f=2+1$ QCD using highly improved staggered quarks (HISQ) with physical masses on $N_\tau=4$, $6$, $8$ lattices. The singularity structure of QCD in the complex $\mu_B$ plane is probed using conserved charges calculated at imaginary $\mu_B$. The location of the singularities is determined by studying the...

We calculate Fourier coefficients of the net-baryon number as a function

of a purely imaginary chemical potential. The asymptotic behavior of

these coefficients is governed by the singularity structure of the QCD

partition function and thus encodes information on phase

transitions. Although it is not easy to obtain a high number of Fourier

coefficients from lattice QCD data directly,...

Knowledge of the screening masses at finite chemical potential can provide insight into the nature of the QCD phase diagram. However, lattice studies at finite chemical potential suffer from the well-known issue of the sign problem, which has made the calculation of observables such as screening correlators and screening masses at finite chemical potential quite challenging. One way to proceed...

In this talk we present our study of the electromagnetic conductivity in dense quark-gluon plasma obtained within lattice simulations with $𝑁_𝑓 = 2 + 1$ dynamical quarks. We employ stout improved rooted staggered quarks at the physical point and the tree-level Symanzik improved gauge action. The simulations are performed at imaginary chemical potential. To reconstruct electromagnetic...

We study the (2+1)-dimensional Gross-Neveu model in an external magnetic field. The model, which serves as a toy model for QCD, has been predicted by mean-field studies to exhibit a very rich phase structure in the plane spanned by temperature and chemical potential as the external field is varied. We investigate what remains of this phase structure beyond the mean-field approximation. Our...

In QCD at large enough isospin chemical potential Bose-Einstein Condensation (BEC) takes place, separated from the normal phase by a phase transition. From previous studies the location of the BEC line at the physical point is known. In the chiral limit the condensation happens already at infinitesimally small isospin chemical potential for zero temperature. The zero-density chiral transition...

At finite baryon chemical potential, the sign problem hinders Monte Carlo simulations which is remedied by a Dual Representation that makes the sign problem mild. At the strong coupling limit, the dual formulation with staggered quarks is well established. We have used this formulation to look at the quark mass dependence of the baryon mass and the nuclear transition which allows us to...

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,

and after a resummation, there is no sign problem

both for non-zero baryon and isospin chemical potential.

We report on recent progress on the...

The thermodynamics of QCD with sufficiently heavy dynamical quarks can be described by a three-dimensional Polyakov loop effective theory, after a truncated character and hopping expansion. We investigate the resulting phase diagram for low temperatures by mean field methods. Taking into account chemical potentials both for baryon number and isospin, we obtain clear signals for a liquid-gas...

At low temperature and large chemical potential QCD might exhibit a chiral inhomogeneous phase, as indicated by various simple low-energy models. One of these models is the 3+1-dimensional Nambu-Jona-Lasinio model, which is non-renormalizable -- rendering the results possibly dependent on the employed regularization scheme. While most previously published results regarding the inhomogeneous...

We studied the 2+1 dimensional XY model at nonzero chemical potential on deformed integration manifolds with the aim of alleviating its sign problem. We investigated several proposals for the deformations and managed to considerably improve on the severity of the sign problem with respect to standard reweighting approaches. In this talk I present numerical evidence that a significant reduction...

We compute the equation of state of isospin asymmetric QCD at zero and non-zero temperatures using direct simulations of lattice QCD with three dynamical flavors at physical quark masses. In addition to the pressure, the trace anomaly and the approach to the continuum, we will particularly discuss the extraction of the speed of sound. Furthermore, we will discuss first steps towards the...

Recently interest in calculations of the speed of sound in QCD under conditions like constant temperature $c_T^2$ or constant entropy per net baryon number $c_s^2$ arose in the discussion of experimental results coming from heavy ion experiments. It has been stressed that the former in particular is closely related to higher order cumulants of conserved charge fluctuations that are calculated...

We update the pressure, energy density and entropy density calculations

at non-zero checmial potentials based on Taylor expansion up to 6th order

performed by the HotQCD Collaboration in 2017.

The HotQCD collaboration has now accumulated an order of magnitude larger

statistics for lattices with temporal extent

Nt=8 and 12 and added results for Nt=16 that were not available...

We present a new way of calculating the QCD equation of state(EoS) at finite chemical potential. Our method derives from the previously published method of exponential resummation. While exponential resummation does resum Taylor coefficients to all orders in $\mu$; on expansion of the series itself, it becomes evident that in addition to genuine higher order contributions, the contribution of...

I will present recent results on the lattice QCD equation of state from the direct

reweighting approach advocated recently in 2004.10800 and 2108.09213. I will present direct results up to a baryochemical potential-to-temperature ratio of $\mu_B/T=3$. I will concentrate on the plasma phase at non-zero baryochemical potential and compare the results with those obtained from different...

We calculate a resummed equation of state with lattice QCD simulations at imaginary chemical potentials. This talk presents a generalization of the scheme introduced in our previous work to the case of non-zero $\mu_S$, focusing on the line of strangeness neutrality.

We present results up to $\mu_B/T \leq 3.5$ on the strangeness neutral line $\left\langle S \right\rangle = 0$ in the...

We present results on the phase diagram of Quantum Chromodynamics (QCD) with two light quark flavours at finite chemical potential from first principle lattice simulations. To circumvent the sign problem we use the complex Langevin method. The pion mass is of approximately 480 MeV. We report on the pressure, energy and entropy equations of state. A particular emphasis is put on the “cold”...

Lattice simulations of non-zero density QCD introduce the so-called sign problem (complex or negative probabilities), which invalidates importance sampling methods. We use the Complex Langevin equation (CLE) to circumvent the sign problem, measure boundary terms and use reweighting to test the reliability of the boundary term observable, confirming expectations from previous studies.

We also...

We obtain the equation of state ($p$ vs. $e$) and the sound velocity ($c_s^2/c^2 = \partial p/\partial e$) for two-color QCD at low temperature and high density and find that in the superfluid phase, $c_s^2/c^2$ becomes larger than $1/3$, which is the value at the relativistic limit. Several independent Monte Carlo studies on $2$-color QCD have been conducted intensively in recent years, and...

We investigate hadron masses in two-color QCD with $N_f=2$ at low temperature and finite density using lattice simulation. We calculate $\pi$ and $\rho$ meson masses and find the flipping of the spectral ordering of these two mesons near the transition between the hadronic and superfluid phases.

Furthermore, we measure hadron masses with isospin $I=0$ and $J^P = 0^{\pm}$. According to the...