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Register a new userTwo-colour QCD at non-zero temperature in the presence of a strong magnetic field
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In this talk we report on our study of two-colour lattice QCD with N_f=4 staggered fermion degrees of freedom with equal electric charge q in a homogeneous magnetic field B at non-zero temperature T. We find indications for a non-monotonic behaviour of the critical temperature as a function of the magnetic field strength and, as a consequence, for the occurence of `inverse magnetic catalysis within the transition region for magnetic fields in the range 0 < qB < 0.7 GeV^2.
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A status of lattice QCD thermodynamics, as of 2013, is summarized. Only bulk thermodynamics is considered. There is a separate section on magnetic fields.
We delineate equilibrium phase structure and topological charge distribution of dense two-colour QCD at low temperature by using a lattice simulation with two-flavour Wilson fermions that has a chemical potential $mu$ and a diquark source $j$ incorporated. We systematically measure the diquark condensate, the Polyakov loop, the quark number density and the chiral condensate with improved accuracy and $jto0$ extrapolation over earlier publications; the known qualitative features of the low temperature phase diagram, which is composed of the hadronic, Bose-Einstein condensed (BEC) and BCS phases, are reproduced. In addition, we newly find that around the boundary between the hadronic and BEC phases, nonzero quark number density occurs even in the hadronic phase in contrast to the prediction of the chiral perturbation theory (ChPT), while the diquark condensate approaches zero in a manner that is consistent with the ChPT prediction. At the highest $mu$, which is of order the inverse of the lattice spacing, all the above observables change drastically, which implies a lattice artifact. Finally, at temperature of order $0.45T_c$, where $T_c$ is the chiral transition temperature at zero chemical potential, the topological susceptibility is calculated from a gradient-flow method and found to be almost constant for all the values of $mu$ ranging from the hadronic to BCS phase. This is a contrast to the case of $0.89T_c$ in which the topological susceptibility becomes small as the hadronic phase changes into the quark-gluon plasma phase.
We present results on the QCD equation of state, obtained with two different improved dynamical staggered fermion actions and almost physical quark masses. Lattice cut-off effects are discussed in detail as results for three different lattice spacings are available now, i.e. results have been obtained on lattices with temporal extent of $N_tau=4,6$ and 8. Furthermore we discuss the Taylor expansion approach to non-zero baryon chemical potential by means of an expansion of the pressure. We use the expansion coefficients to calculate various fluctuations and correlations among hadronic charges. We find that the correlations reproduce the qualitative behavior of the resonance gas model below $T_c$ and start to agree with the free gas predictions for $Tgsim 1.5T_c$.
We present results for pseudo-critical temperatures of QCD chiral crossovers at zero and non-zero values of baryon ($B$), strangeness ($S$), electric charge ($Q$), and isospin ($I$) chemical potentials $mu_{X=B,Q,S,I}$. The results were obtained using lattice QCD calculations carried out with two degenerate up and down dynamical quarks and a dynamical strange quark, with quark masses corresponding to physical values of pion and kaon masses in the continuum limit. By parameterizing pseudo-critical temperatures as $ T_c(mu_X) = T_c(0) left[ 1 -kappa_2^{X}(mu_{X}/T_c(0))^2 -kappa_4^{X}(mu_{X}/T_c(0))^4 right] $, we determined $kappa_2^X$ and $kappa_4^X$ from Taylor expansions of chiral observables in $mu_X$. We obtained a precise result for $T_c(0)=(156.5pm1.5);mathrm{MeV}$. For analogous thermal conditions at the chemical freeze-out of relativistic heavy-ion collisions, i.e., $mu_{S}(T,mu_{B})$ and $mu_{Q}(T,mu_{B})$ fixed from strangeness-neutrality and isospin-imbalance, we found $kappa_2^B=0.012(4)$ and $kappa_4^B=0.000(4)$. For $mu_{B}lesssim300;mathrm{MeV}$, the chemical freeze-out takes place in the vicinity of the QCD phase boundary, which coincides with the lines of constant energy density of $0.42(6);mathrm{GeV/fm}^3$ and constant entropy density of $3.7(5);mathrm{fm}^{-3}$.
In this contribution we revisit simulations of two-color QCD with rooted staggered quarks at finite density, where baryon-number spontaneously breaks and a diquark condensate forms. We thereby pay special attention to simulating outside the lattice-artifact bulk phase, in which $Z_2$ monopoles condense, and investigate some of the consequences of this, e.g. on the chiral and the diquark condensate which were known to be well described by chiral effective field theory. Not surprisingly, on finer lattices outside the bulk phase the quark condensate now requires additive renormalization before it can be compared with effective field theory predictions. The subtraction must necessarily depend on the chemical potential, however. The diquark condensate is not affected by this problem and remains in good agreement with these predictions. We also compare staggered with Wilson quarks to demonstrate that the two fermion discretizations yield qualitatively different results well below half-filling already. We close with prelimiary results for the Goldstone spectrum to demonstrate that the continuum pattern is recovered also with staggered quarks outside the bulk phase.
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