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Register a new userQCD simulations at small chemical potential
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Within the reweighting approach, one has the freedom to choose the Monte Carlo action so that it provides a good overlap with the finite-mu measure but remains simple to simulate. We explore several choices of action in the regime of small mu. Simulating with a finite isospin chemical potential mu_I=mu gives a better overlap than the standard choice mu=0, with no computational overhead.
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We provide the most accurate results for the QCD transition line so far. We optimize the definition of the crossover temperature $T_c$, allowing for its very precise determination, and extrapolate from imaginary chemical potential up to real $mu_B approx 300$ MeV. The definition of $T_c$ adopted in this work is based on the observation that the chiral susceptibility as a function of the condensate is an almost universal curve at zero and imaganiary $mu_B$. We obtain the parameters $kappa_2=0.0153(18)$ and $kappa_4=0.00032(67)$ as a continuum extrapolation based on $N_t=10,12$ and $16$ lattices with physical quark masses. We also extrapolate the peak value of the chiral susceptibility and the width of the chiral transition along the crossover line. In fact, both of these are consistent with a constant function of $mu_B$. We see no sign of criticality in the explored range.
We investigate the properties of QCD at finite isospin chemical potential at zero and non-zero temperatures. This theory is not affected by the sign problem and can be simulated using Monte-Carlo techniques. With increasing isospin chemical potential and temperatures below the deconfinement transition the system changes into a phase where charged pions condense, accompanied by an accumulation of low modes of the Dirac operator. The simulations are enabled by the introduction of a pionic source into the action, acting as an infrared regulator for the theory, and physical results are obtained by removing the regulator via an extrapolation. We present an update of our study concerning the associated phase diagram using 2+1 flavours of staggered fermions with physical quark masses and the comparison to Taylor expansion. We also present first results for our determination of the equation of state at finite isospin chemical potential and give an example for a cosmological application. The results can also be used to gain information about QCD at small baryon chemical potentials using reweighting with respect to the pionic source parameter and the chemical potential and we present first steps in this direction.
We study the density of states method as well as reweighting to explore the low temperature phase diagram of QCD at finite baryon chemical potential. We use four flavors of staggered quarks, a tree-level Symanzik improved gauge action and four stout smearing steps on lattices with $N_s=4,6,8$ and $N_t=6 - 16$. We compare our results to that of the phase quenched ensemble and also determine the pion and nucleon masses. In the density of states approach we applied pion condensate or gauge action density fixing. We found that the density of states method performs similarly to reweighting. At $T approx 100$ MeV, we found an indication of the onset of the quark number density at around $mu/m_N sim 0.16 - 0.18$ on $6^4$ lattices at $beta=2.9$.
We present results for the QCD equation of state, quark densities and susceptibilities at nonzero chemical potential, using 2+1 flavor asqtad ensembles with $N_t=4$. The ensembles lie on a trajectory of constant physics for which $m_{ud}approx0.1m_s$. The calculation is performed using the Taylor expansion method with terms up to sixth order in $mu/T$.
In this lecture we discuss various properties of the phase factor of the fermion determinant for QCD at nonzero chemical potential. Its effect on physical observables is elucidated by comparing the phase diagram of QCD and phase quenched QCD and by illustrating the failure of the Banks-Casher formula with the example of one-dimensional QCD. The average phase factor and the distribution of the phase are calculated to one-loop order in chiral perturbation theory. In quantitative agreement with lattice QCD results, we find that the distribution is Gaussian with a width $sim mu T sqrt V$ (for $m_pi ll T ll Lambda_{rm QCD}$). Finally, we introduce, so-called teflon plated observables which can be calculated accurately by Monte Carlo even though the sign problem is severe.
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