Lattice QCD at Non-Zero Temperature

This is a review of selected recent developments in finite-temperature lattice QCD. The focus is on the properties of the chiral crossover region, deconfinement and fluctuations of conserved charges, the equation of state, properties of heavy quarkonia and reconstruction of spectral functions.Comment: 20 pages, 23 figures, plenary talk presented at the 32nd International Symposium on Lattice Field Theory, June 23-28, 2014, Columbia University, New York City, N

The QCD equation of state with 2+1 flavors of Highly Improved Staggered Quarks (HISQ)

One of the fundamental properties of the quark-gluon plasma (QGP), the equation of state, is a subject of extensive studies in lattice QCD and an essential requirement for the correct hydrodynamic modeling of heavy-ion collisions. Lattice QCD provides first-principle calculations for the physics in the non-perturbative regime. In this contribution, we report on recent progress by the HotQCD collaboration in studying the 2+1 flavor equation of state on lattices with the temporal extent N_tau=6, 8, 10 and 12 in Highly Improved Staggered Quarks (HISQ) discretization scheme. Comparisons with equation of state calculations with different fermion actions are also discussed.Comment: 4 pages, 4 figures, talk presented at the Quark Matter 2012 International Conference, Washington D.C., Aug 13-18, 201

An overview of (selected) recent results in finite-temperature lattice QCD

I discuss recent results on lattice QCD calculations with the main emphasis on the thermodynamics of the crossover region, restoration of the chiral symmetry and fluctuations of conserved charges as indicator of deconfinement, that may also be used to determine the chemical freeze-out conditions in heavy-ion collision experiments.Comment: Talk presented at Hot Quarks 2012, to be published in the proceedings, 6 pages, 8 figure

First results on QCD thermodynamics with HISQ action

We report on investigations of the chiral and deconfinement aspects of the finite temperature transition in 2+1 flavor QCD using the Highly Improved Staggered Quark (HISQ) action on lattices with temporal extent $N_\tau=6$ and $N_\tau=8$. We have calculated several physical observables, including the renormalized Polyakov loop, strangeness fluctuations, the renormalized chiral condensate and the chiral susceptibility in the crossover region for physical values of the strange quark mass $m_s$ and light quark masses $m_l=0.2m_s$ and $0.05m_s$. We compare our findings with previous calculations that use different improved staggered fermion formulations: asqtad, p4 and stout.Comment: 7 pages, 4 figures, talk presented at the XXVII International Symposium on Lattice Field Theory, July 26-31, 2009, Peking University, Beijing, Chin

Deconfinement and chiral transition with the highly improved staggered quark (HISQ) action

We report on investigations of the chiral and deconfinement aspects of the finite temperature transition in 2+1 flavor QCD using the Highly Improved Staggered Quark (HISQ) action on lattices with temporal extent $N_\tau=6$ and $N_\tau=8$. We have performed the calculations for physical values of the strange quark mass $m_s$ and the light quark masses $m_l=0.2m_s$ and $0.05m_s$. Several finite temperature observables, including the renormalized Polyakov loop, the renormalized chiral condensate and the chiral susceptibility have been calculated. We also study the fluctuations and correlations of different conserved charges as well as the trace anomaly at finite temperature. We compare our findings with previous calculations that use different improved staggered fermion formulations: asqtad, p4 and stout.Comment: 16 pages, 17 figures, talk presented at the 26th Winter Workshop on Nuclear Dynamics, Ocho Rios, Jamaica, January 2-9, 2010, to be published in Journal of Physics: Conference Series (JPCS

Taste symmetry and QCD thermodynamics with improved staggered fermions

Taste symmetry violations in staggered fermion formulations correlate strongly with the cut-off (lattice spacing) dependence in thermodynamic quantities. Better taste symmetry on the lattice can be achieved either by decreasing the lattice spacing and going to larger temporal extent in finite-temperature calculations, or by further improving the action. The highly improved staggered quark (HISQ) action offers a further degree of improvement and substantially reduces taste violations. We report on our studies of the 2+1 flavor QCD thermodynamics with the HISQ/tree action. By systematically comparing HISQ/tree, asqtad, p4 and stout calculations we quantify how the cut-off effects manifest themselves in different thermodynamic quantities, including the renormalized Polyakov loop, chiral condensate, various fluctuations and correlations of conserved charges. The implications for the equation of state and a comparison to the hadron resonance gas model are also discussed. The chiral aspects of the finite-temperature transition are discussed in the companion HotQCD contribution [1].Comment: 7 pages, 7 figures, talk presented at the XXVIII International Symposium on Lattice Field Theory, June 14-19, 2010, Villasimius, Sardinia, Ital

Critical Exponents for U(1) Lattice Gauge Theory at Finite Temperature

For compact U(1) lattice gauge theory (LGT) we have performed a finite size scaling analysis on $N_{\tau} N_s^3$ lattices for $N_{\tau}$ fixed and $N_s\to\infty$, approaching the phase transition from the confined phase. For $N_{\tau}=4$, 5 and 6 our data contradict the expected scenario that this transition is either first order or in the universality class of the 3d XY model. If there are no conceptional flaws in applying the argument that the Gaussian fixed point in 3d is unstable to our systems, estimates of the critical exponents $\alpha/\nu$, $\gamma/\nu$, $(1-\beta)/\nu$ and $2-\eta$ indicate the existence of a new, non-trivial renormalization group fixed point for second order phase transitions in 3d. Such a fixed point would be of importance for renormalization group theory and statistical physics.Comment: Lattice Conference, July 23-28, 2006 Tucson, Arizona, USA. 7 pages, 3 figure

SU(3) Deconfining Phase Transition in a Box with Cold Boundaries

Deconfined regions created in heavy ion collisions are bordered by the confined phase. We discuss boundary conditions (BCs) to model a cold exterior. Monte Carlo simulations of pure SU(3) lattice gauge theory with thus inspired BCs show scaling. Corrections to usual results survive in the finite volume continuum limit and we estimate them in a range from L=5-10 fermi as function of the volume size $L^3$. In magnitude these corrections are comparable to those obtained by including quarks.Comment: The XXV International Symposium on Lattice Field Theory, July 30 - August 4 2007, Regensburg, Germany. 7 pages, 3 figure

Commutator-free Lie group methods with minimum storage requirements and reuse of exponentials

A new format for commutator-free Lie group methods is proposed based on explicit classical Runge-Kutta schemes. In this format exponentials are reused at every stage and the storage is required only for two quantities: the right hand side of the differential equation evaluated at a given Runge-Kutta stage and the function value updated at the same stage. The next stage of the scheme is able to overwrite these values. The result is proven for a 3-stage third order method and a conjecture for higher order methods is formulated. Five numerical examples are provided in support of the conjecture.Comment: 42 pages, 10 figure