arXiv subjects

Owe Philipsen

Publications and source records attributed to Owe Philipsen.

At least 91 records · Page 5Linked to original sources

arXiv2016

A real-time lattice simulation of the thermalization of a gluon plasma: first results

To achieve an understanding of the thermalization of a quark-gluon plasma, starting from QCD without using model assumptions, is a formidable task. We study the early stage dynamics of a relativistic heavy ion collision in the framework of real time simulations of classical Yang-Mills theory in a static box with the color glass condensate as initial condition. Our study generalizes a previous one by Fukushima and Gelis from SU(2) to the realistic case of SU(3). We calculate the chromo-electric and chromo-magnetic energy densities as well as the ratio of longitudinal and transverse pressure as a function of time as probes for thermalization. Our preliminary results on coarse lattices show the occurrence of Weibel instabilities prior to thermalization.

hep-ph↗

arXiv2016

Roberge-Weiss transition in $N_\text{f}=2$ QCD with Wilson fermions and $N_τ=6$

QCD with imaginary chemical potential is free of the sign problem and exhibits a rich phase structure constraining the phase diagram at real chemical potential. We simulate the critical endpoint of the Roberge-Weiss (RW) transition at imaginary chemical potential for $N_\text{f}=2$ QCD on $N_τ=6$ lattices with standard Wilson fermions. As found on coarser lattices, the RW endpoint is a triple point connecting the deconfinement/chiral transitions in the heavy/light quark mass regions and changes to a second-order endpoint for intermediate masses. These regimes are separated by two tricritical values of the quark mass, which we determine by extracting the critical exponent $ν$ from a systematic finite size scaling analysis of the Binder cumulant of the imaginary part of the Polyakov loop. We are able to explain a previously observed finite size effect afflicting the scaling of the Binder cumulant in the regime of three-phase coexistence. Compared to $N_τ=4$ lattices, the tricritical masses are shifted towards smaller values. Exploratory results on $N_τ=8$ as well as comparison with staggered simulations suggest that significantly finer lattices are needed before a continuum extrapolation becomes feasible.

hep-lat↗

arXiv2016

Equation of state for cold and dense heavy QCD

A previously derived three-dimensional effective lattice theory describing the thermodynamics of QCD with heavy quarks in the cold and dense region is extended through order $\sim u^5κ^8$ in the combined character and hopping expansion of the original four-dimensional Wilson action. The systematics of the effective theory is investigated to determine its range of validity in parameter space. We demonstrate the severe cut-off effects due to lattice saturation, which afflict any lattice results at finite baryon density independent of the sign problem or the quality of effective theories, and which have to be removed by continuum extrapolation. We then show how the effective theory can be solved analytically by means of a linked cluster expansion, which is completely unaffected by the sign problem, in quantitative agreement with numerical simulations. As an application, we compute the cold nuclear equation of state of heavy QCD. Our continuum extrapolated result is consistent with a polytropic equation of state for non-relativistic fermions.

hep-lat↗

arXiv2015

The nature of the Roberge-Weiss Transition in $N_f=2$ QCD with Wilson Fermions on $N_τ=6$ lattices

The finite temperature chiral and deconfinement phase transitions at zero density for light and heavy quarks, respectively, have analytic continuations to imaginary chemical potential. At some critical imaginary chemical potential, they meet the Roberge-Weiss transition between adjacent $Z(3)$ sectors. For light and heavy quarks, where the chiral and deconfinement transitions are first order, the transition lines meet in a triple point. For intermediate masses chiral or deconfinement transitions are crossover and the Roberge-Weiss transition ends in a second order point. At the boundary between these regimes the junction is a tricritical point, as shown in studies with $N_f=2,3$ flavors of staggered and Wilson quarks on $N_τ=4$ lattices. Employing finite size scaling we investigate the nature of this point as a function of quark mass for $N_f=2$ flavors of Wilson fermions with a temporal lattice extent of $N_τ=6$. In particular we are interested in the change of the location of tricritical points compared to our ealier study on $N_τ=4$.

hep-lat↗

arXiv2015

Heavy dense QCD from a 3d effective lattice theory

The cold and dense regime of the QCD phase diagram is to this day inaccessible to first principle lattice calculations owing to the sign problem. Here we present progress of an ongoing effort to probe this particularly difficult regime utilising a dimensionally reduced effective lattice theory with a significantly reduced sign problem. The effective theory is derived by combined character and hopping expansion and is valid for heavy quarks near the continuum. We show an extension of the effective theory to order $u^5κ^8$ in the cold regime. A linked cluster expansion is applied to the effective theory resulting in a consistent mechanism for handling the effective theory fully analytically. The new results are consistent with the ones from simulations confirming the viability of analytic methods. Finally we resum the analytical result which doubles the convergence region of the expansion.

hep-lat↗

arXiv2015

The $N_f= 2$ chiral phase transition from imaginary chemical potential with Wilson Fermions

The order of the thermal transition in the chiral limit of QCD with two dynamical flavours of quarks is a long-standing issue. Still, it is not definitely known whether the transition is of first or second order in the continuum limit. Which of the two scenarios is realized has important implications for the QCD phase diagram and the existence of a critical endpoint at finite densities. Settling this issue by simulating at successively decreased pion mass was not conclusive yet. Recently, an alternative approach was proposed, extrapolating the first order phase transition found at imaginary chemical potential to zero chemical potential with known exponents, which are induced by the Roberge-Weiss symmetry. For staggered fermions on $N_t=4$ lattices, this results in a first order transition in the chiral limit. Here we report of $N_t=4$ simulations with Wilson fermions, where the first order region is found to be large.

hep-lat↗

arXiv2015

Numerical corrections to the strong coupling effective Polyakov-line action for finite T Yang-Mills theory

We consider a three-dimensional effective theory of Polyakov lines derived previously from lattice Yang-Mills theory and QCD by means of a resummed strong coupling expansion. The effective theory is useful for investigations of the phase structure, with a sign problem mild enough to allow simulations also at finite density. In this work we present a numerical method to determine improved values for the effective couplings directly from correlators of the 4d Yang-Mills theory. For values of the gauge coupling up to the vicinity of the phase transition, the dominant short range effective coupling are well described by their corresponding strong coupling series. We provide numerical results also for the longer range interactions, Polyakov lines in higher representations as well as four-point interactions, and discuss the growing significance of non-local contributions as the lattice gets finer. Within this approach the critical Yang-Mills coupling $β_c$ is reproduced to better than one percent from a one-coupling effective theory on $N_τ=4$ lattices while up to five couplings are needed on $N_τ=8$ for the same accuracy.

hep-lat↗

arXiv2015

QCD phase diagram from the lattice at strong coupling

The phase diagram of lattice QCD in the strong coupling limit can be measured in the full $μ$-$T$ plane, also in the chiral limit. In particular, the phase diagram in the chiral limit features a tricritical point at some $(μ_c,T_c)$. This point may be related to the critical end point expected in the QCD phase diagram. We discuss the gauge corrections to the phase diagram at strong coupling and compare our findings with various possible scenarios in continuum QCD. We comment on the possibility that the tricritical point at strong coupling is connected to the tricritical point in the continuum, massless QCD.

hep-lat↗

arXiv2014

CL2QCD - Lattice QCD based on OpenCL

We present the Lattice QCD application CL2QCD, which is based on OpenCL and can be utilized to run on Graphic Processing Units as well as on common CPUs. We focus on implementation details as well as performance results of selected features. CL2QCD has been successfully applied in LQCD studies at finite temperature and density and is available at http://code.compeng.uni-frankfurt.de/projects/clhmc .

hep-lat↗

arXiv2014

The chiral phase transition in two-flavor QCD from imaginary chemical potential

We investigate the order of the finite temperature chiral symmetry restoration transition for QCD with two massless fermions, by using a novel method, based on simulating imaginary values of the quark chemical potential $μ=iμ_i,μ_i\in\mathbb{R}$. Our method exploits the fact that, for low enough quark mass $m$ and large enough chemical potential $μ_i$, the chiral transition is decidedly first order, then turning into crossover at a critical mass $m_c(μ)$. It is thus possible to determine the critical line in the $m - μ^2$ plane, which can be safely extrapolated to the chiral limit by taking advantage of the known tricritical indices governing its shape. We test this method with standard staggered fermions and the result of our simulations is that $m_c(μ=0)$ is positive, so that the phase transition at zero density is definitely first order in the chiral limit, on our coarse $N_t=4$ lattices with $a\simeq 0.3\,\mathrm{fm}$.

hep-lat↗

arXiv2014

The lattice QCD phase diagram in and away from the strong coupling limit

We study lattice QCD with four flavors of staggered quarks. In the limit of infinite gauge coupling, "dual" variables can be introduced, which render the finite-density sign problem mild and allow a full determination of the $μ-T$ phase diagram by Monte Carlo simulations, also in the chiral limit. However, the continuum limit coincides with the weak coupling limit. We propose a strong-coupling expansion approach towards the continuum limit. We show first results, including the phase diagram and its chiral critical point, from this expansion truncated to next-to-leading order.

hep-lat↗

arXiv2014

Heavy dense QCD and nuclear matter from an effective lattice theory

A three-dimensional effective lattice theory of Polyakov loops is derived from QCD by expansions in the fundamental character of the gauge action, u, and the hopping parameter, κ, whose action is correct to κ^n u^m with n+m=4. At finite baryon density, the effective theory has a sign problem which meets all criteria to be simulated by complex Langevin as well as by Monte Carlo on small volumes. The theory is valid for the thermodynamics of heavy quarks, where its predictions agree with simulations of full QCD at zero and imaginary chemical potential. In its region of convergence, it is moreover amenable to perturbative calculations in the small effective couplings. In this work we study the challenging cold and dense regime. We find unambiguous evidence for the nuclear liquid gas transition once the baryon chemical potential approaches the baryon mass, and calculate the nuclear equation of state. In particular, we find a negative binding energy per nucleon causing the condensation, whose absolute value decreases exponentially as mesons get heavier. For decreasing meson mass, we observe a first order liquid gas transition with an endpoint at some finite temperature, as well as gap between the onset of isospin and baryon condensation.

hep-lat↗

arXiv2014

The nature of the Roberge-Weiss transition in $N_f=2$ QCD with Wilson fermions

At imaginary values of the quark chemical potential $μ$, Quantum Chromodynamics shows an interesting phase structure due to an exact center, or Roberge-Weiss (RW), symmetry. This can be used to constrain QCD at real $μ$, where the sign problem prevents Monte Carlo simulations of the lattice theory. In previous studies of this region with staggered fermions it was found that the RW endpoint, where the center transition changes from first-order to a crossover, depends non-trivially on the quark mass: for high and low masses, it is a triple point connecting to the deconfinement and chiral transitions, respectively, changing to a second-order endpoint for intermediate mass values. These parameter regions are separated by tricritical points. Here we present a confirmation of these findings using Wilson fermions on $N_τ=4$ lattices. In addition, our results provide a successful quantitative check for a heavy quark effective lattice theory at finite density.

hep-lat↗

arXiv2014

The Phase Diagram of Strong Coupling QCD including Gauge Corrections

The strong coupling limit of lattice QCD with staggered fermions has been studied for decades, both via Monte Carlo and via mean field theory. In this model, the finite density sign problem can be made mild and the full phase diagram can be obtained, even in the chiral limit. It is however desirable to understand the effect of a finite lattice gauge coupling $β$ on the phase diagram in the $μ-T$ plane in order to understand how it evolves into the phase diagram of continuum QCD. Here we discuss how to construct a partition function for non-zero lattice coupling, exact to $\mathcal{O}(β)$, and present corresponding Monte Carlo results, in particular for corrections to the chiral susceptibility and to the phase diagram.

hep-lat↗

arXiv2014

The second order hydrodynamic transport coefficient $κ$ for the gluon plasma from the lattice

The quark gluon plasma produced in heavy ion collisions behaves like an almost ideal fluid described by viscous hydrodynamics with a number of transport coefficients. The second order coefficient $κ$ is related to a Euclidean correlator of the energy-momentum tensor at vanishing frequency and low momentum. This allows for a lattice determination without maximum entropy methods or modelling, but the required lattice sizes represent a formidable challenge. We calculate $κ$ in leading order lattice perturbation theory and simulations on $120^3\times 6,8$ lattices with $a<0.1$ fm. In the temperature range $2T_\mathrm{c}-10T_\mathrm{c}$ we find $κ=0.36(15)T^2$. The error covers both a suitably rescaled AdS/CFT prediction as well as, remarkably, the result of leading order perturbation theory. This suggests that appropriate noise reduction methods on the lattice and NLO perturbative calculations could provide an accurate QCD prediction in the near future.

hep-lat↗

arXiv2013

Effective lattice Polyakov loop theory vs. full SU(3) Yang-Mills at finite temperature

A three-dimensional effective theory of Polyakov loops has recently been derived from Wilson's Yang-Mills lattice action by means of a strong coupling expansion. It is valid in the confined phase up to the deconfinement phase transition, for which it predicts the correct order and gives quantitative estimates for the critical coupling. In this work we study its predictive power for further observables like correlation functions and the equation of state. We find that the effective theory correctly reproduces qualitative features and symmetries of the full theory as the continuum is approached. Regarding quantitative predictions, we identify two classes of observables by numerical comparison as well as analytic calculations: correlation functions and their associated mass scales cannot be described accurately from a truncated effective theory, due to its inherently non-local nature involving long-range couplings. On the other hand, phase transitions and bulk thermodynamic quantities are accurately reproduced by the leading local part of the effective theory. In particular, the effective theory description is numerically superior when computing the equation of state at low temperatures or the properties of the phase transition.

hep-lat↗

arXiv2013

Effective lattice Polyakov loop theory for finite temperature Yang-Mills

Effective Polyakov loop theories are a useful tool for an investigation of pure Yang-Mills theory and full QCD. A systematic derivation of the effective action can be done in a spatial strong coupling expansion. Quite accurate predictions for the deconfinement phase transition of Yang-Mills theory have been obtained in this approach. Besides the critical couplings, further observables can be measured in the effective theory. These provide additional tests for the reliability of the strong coupling approach and the truncation of the effective action. In this contribution we will present recent results for the free energy of the static quark-antiquark pair and the equation of state.

hep-lat↗

arXiv2013

Onset Transition to Cold Nuclear Matter from Lattice QCD with Heavy Quarks to $κ^4$

We present results of our ongoing studies of an effective three-dimensional theory of thermal lattice QCD with heavy Wilson quarks. This is done by combined strong coupling and hopping parameter expansions. The full quark determinant of four dimensional lattice QCD is expanded in orders of the hopping parameter $κ$, the dimensional reduction is achieved by integrating over the spatial links. We present the calculation of the effective theory through order $κ^nu^m$ with $n+m=4$. This theory is then used to simulate heavy quarks near the cold and dense limit. For nonzero chemical potential the theory suffers from a sign problem, wich is avoided by employing stochastical quantisation. Continuum extrapolated results for the onset of nuclear matter are shown and the region of convergence of the effective theory is discussed.

hep-lat↗