arXiv subjects

Lorenz von Smekal

Publications and source records attributed to Lorenz von Smekal.

At least 73 records · Page 4Linked to original sources

arXiv2015

Lattice simulations of $G_2$-QCD at finite density

$G_2$-QCD, in which the exceptional Lie group $G_2$ replaces the $SU(3)$ gauge group of QCD, does not suffer from a fermion sign problem. It can therefore be simulated also at comparatively low temperatures and high densities on the lattice, which hence allows to map out the phase diagram of this QCD-like theory. We briefly review some of our previous results from such finite density simulations to then present further evidence for a first-order transition to what might be called $G_2$-nuclear matter. In order to isolate diquark condensation effects, we introduce simulations with Majorana fermions and diquark sources. This allows to disentangle states in the spectrum that are connected by charge conjugation. We discuss chiral symmetry in the presence of diquark sources and present first results from our ongoing large-scale simulations.

hep-lat↗

arXiv2014

Effective SU(2) Polyakov Loop Theories with Heavy Quarks on the Lattice

We compare SU(2) Polyakov loop models with different effective actions with data from full two-color QCD simulations around and above the critical temperature. We then apply the effective theories at finite temperature and density to extract quantities like Polyakov loop correlators, effective Polyakov loop potentials and baryon density.

hep-lat↗

arXiv2014

Flow equations for spectral functions at finite external momenta

In this work we study the spatial-momentum dependence of mesonic spectral functions obtained from the quark-meson model using a recently proposed method to calculate real-time observables at finite temperature and density from the Functional Renormalization Group. This non-perturbative method is thermodynamically consistent, symmetry-preserving and based on an analytic continuation from imaginary to real time on the level of the flow equations for 2-point functions. Results on the spatial-momentum dependence of the pion and sigma spectral function are presented at different temperatures and densities, in particular near the critical endpoint in the phase diagram of the quark-meson model.

hep-ph↗

arXiv2014

On the semimetal-insulator transition and Lifshitz transition in simulations of mono-layer graphene

We report on the status of ongoing Hybrid-Monte-Carlo simulations of the tight-binding model of mono-layer graphene. We present results concerning the semimetal-insulator phase transition, whereby two-body interactions are modeled by a partially screened Coulomb potential which takes into account screening by electrons in the lower $σ$-orbitals. We obtain evidence that finite-size effects may still be present in the current estimate of the critical coupling strength $α_C$, which was previously extracted from simulations on lattice-sizes up to $N_x=N_y=18$. We also present preliminary results concerning the Neck-disrupting Lifshitz transition which occurs at finite Fermion-density in the limit of vanishing two-body interactions. A sign-problem is circumvented by using a spin-dependent chemical potential in our simulations.

hep-lat↗

arXiv2014

Spectral functions from the functional renormalization group at finite temperature and density

We present a viable method to obtain real-time quantities such as spectral functions or transport coefficients at finite temperature and density within a non-perturbative Functional Renormalization Group approach. Our method is based on a thermodynamically consistent truncation of the flow equations for 2-point functions with analytically continued frequency components in the originally Euclidean external momenta. We demonstrate its feasibility by calculating the mesonic spectral functions in the quark-meson model at different temperatures and quark chemical potentials, in particular around the critical endpoint in the phase diagram of the model.

hep-ph↗

arXiv2014

Spurious divergences in Dyson-Schwinger equations

We revisit the treatment of spurious ultraviolet divergences in the equation of motion of the gluon propagator caused by a momentum cutoff and the resulting violation of gauge invariance. With present continuum studies of the gluon propagator from its Dyson-Schwinger equation reaching the level of quantitatively accurate descriptions, it becomes increasingly important to understand how to subtract these spurious divergences in an unambiguous way. Here we propose such a method. It is based entirely on the asymptotic perturbative behavior of the QCD Green's functions without affecting non-perturbative aspects such as mass terms or the asymptotic infrared behavior. As a particular example, this allows us to assess the possible influence of the tadpole diagram beyond perturbation theory. Finally, we test this method numerically by solving the system of Dyson-Schwinger equations of the gluon and ghost propagators.

hep-ph↗

arXiv2014

Spectral Functions from the Functional Renormalization Group

In this article we wish to present a new method to obtain spectral functions at finite temperature and density from the Functional Renormalization Group (FRG). The FRG offers a powerful non-perturbative tool to deal with phase transitions in strong-interaction matter under extreme conditions and their fluctuation properties. Based on a thermodynamically consistent truncation we derive flow equations for pertinent two-point functions in Minkowski space-time. We demonstrate the feasibility of the method by calculating mesonic spectral functions in hot and dense hadronic matter using the quark-meson model as a simple example.

hep-ph↗

arXiv2014

Gluonic three-point correlations in pure Landau gauge QCD

We report on the first self-consistent solution of the Dyson-Schwinger equation (DSE) for the three-gluon vertex. Based on earlier results for the propagators which match data from lattice Monte-Carlo simulations, we obtain results for the three-gluon vertex that are in very good agreement with available lattice data likewise. Feeding these results back into the propagator DSEs leads to some changes especially in the gluon propagator. These changes allow us to assess previously used models for the three-gluon vertex and to systematically estimate the influence of neglected two-loop diagrams with four-gluon interactions. In the final step, a full iterative solution to the coupled DSEs of pure Landau gauge QCD without quarks is then obtained for the first time in an extended truncation which now dynamically includes the complete set of three-point vertex functions.

hep-ph↗

arXiv2014

Polyakov-Quark-Meson-Diquark Model for two-color QCD

We present an update on the phase diagram of two-color QCD from a chiral effective model approach based on a quark-meson-diquark model using the Functional Renormalization Group (FRG). We discuss the impact of perturbative UV contributions, the inclusion of gauge field dynamics via a phenomenological Polyakov loop potential, and the impact of matter backcoupling on the gauge sector. The corresponding phase diagram including these effects is found to be in qualitative agreement with recent lattice investigations.

hep-ph↗

arXiv2014

Real-Time Correlation Functions in the O(N) Model from the Functional Renormalization Group

In the framework of the functional renormalization group (FRG) we present a simple truncation scheme for the computation of real-time mesonic n-point functions, consistent with the derivative expansion of the effective action. Via analytic continuation on the level of the flow equations we perform calculations of mesonic spectral functions in the scalar O(N) model, which we use as an exploratory example. By investigating the renormalization-scale dependence of the 2-point functions we shed light on the nature of the sigma meson, whose spectral properties are predominantly of dynamical origin.

hep-ph↗

arXiv2014

Monte-Carlo simulation of the tight-binding model of graphene with partially screened Coulomb interactions

We report on Hybrid-Monte-Carlo simulations of the tight-binding model with long-range Coulomb interactions for the electronic properties of graphene. We investigate the spontaneous breaking of sublattice symmetry corresponding to a transition from the semimetal to an antiferromagnetic insulating phase. Our short-range interactions thereby include the partial screening due to electrons in higher energy states from ab initio calculations based on the constrained random phase approximation [T.O.Wehling {\it et al.}, Phys.Rev.Lett.{\bf 106}, 236805 (2011)]. In contrast to a similar previous Monte-Carlo study [M.V.Ulybyshev {\it et al.}, Phys.Rev.Lett.{\bf 111}, 056801 (2013)] we also include a phenomenological model which describes the transition to the unscreened bare Coulomb interactions of graphene at half filling in the long-wavelength limit. Our results show, however, that the critical coupling for the antiferromagnetic Mott transition is largely insensitive to the strength of these long-range Coulomb tails. They hence confirm the prediction that suspended graphene remains in the semimetal phase when a realistic static screening of the Coulomb interactions is included.

hep-lat↗

arXiv2014

On propagators and vertices of Landau gauge Yang-Mills theory

We calculate the three-point functions of pure Landau gauge QCD and investigate their influence on the propagators. As expected, the ghost-gluon vertex leads only to minor modifications, while the three-gluon vertex has a sizeable impact on the mid-momentum regime of the gluon propagator. We describe an effective model of the three-gluon vertex that includes contributions from the neglected two-loop diagrams and thus allows to obtain propagators in good agreement with lattice results. We also determine the three-gluon vertex from these propagators and find good agreement with lattice results as well. In turn, these results allow us to assess the effect of the missing two-loop diagrams in the gluon propagator equation. Finally, we present the first self-consistent calculation that includes all two-and three-point functions.

hep-ph↗

arXiv2013

Hadron masses and baryonic scales in $G_2$-QCD at finite density

The QCD phase diagram at densities relevant to neutron stars remains elusive, mainly due to the fermion-sign problem. At the same time, a plethora of possible phases has been predicted in models. Meanwhile $G_2$-QCD, for which the $SU(3)$ gauge group of QCD is replaced by the exceptional Lie group $G_2$, does not have a sign problem and can be simulated at such densities using standard lattice techniques. It thus provides benchmarks to models and functional continuum methods, and it serves to unravel the nature of possible phases of strongly interacting matter at high densities. Instrumental in understanding these phases is that $G_2$-QCD has fermionic baryons, and that it can therefore sustain a baryonic Fermi surface. Because the baryon spectrum of $G_2$-QCD also contains bosonic diquark and probably other more exotic states, it is important to understand this spectrum before one can disentangle the corresponding contributions to the baryon density. Here we present the first systematic study of this spectrum from lattice simulations at different quark masses. This allows us to relate the mass hierarchy, ranging from scalar would-be-Goldstone bosons and intermediate vector bosons to the $G_2$-nucleons and deltas, to individual structures observed in the total baryon density at finite chemical potential.

hep-lat↗

arXiv2013

Finite-Temperature Spectral Functions from the Functional Renormalization Group

We present a method to obtain spectral functions at finite temperature from the Functional Renormalization Group. Our method is based on a thermodynamically consistent truncation of the flow equations for 2-point functions with analytically continued frequency components in the originally Euclidean external momenta. For the uniqueness of this continuation at finite temperature we furthermore implement the physical Baym-Mermin boundary conditions. Results are presented for mesonic spectral functions obtained from a two-flavor quark-meson model.

hep-lat↗

arXiv2013

Chiral restoration and deconfinement in two-color QCD with two flavors of staggered quarks

In preparation of lattice studies of the two-color QCD phase diagram we study chiral restoration and deconfinement at finite temperature with two flavors of staggered quarks using an RHMC algorithm on GPUs. We first study unquenching effects in local Polyakov loop distributions, and the Polyakov loop potential obtained via Legendre transformation, in a fixed-scale approach for heavier quarks. We also present the chiral condensate and the corresponding susceptibility over the lattice coupling across the chiral transition for lighter quarks. Using Ferrenberg-Swendsen reweighting we extract the maxima of the chiral susceptibility in order to determine pseudo-critical couplings on various lattices suitable for chiral extrapolations. These are then used to fix the relation between coupling and temperature in the chiral limit.

hep-lat↗

arXiv2013

Fractional Charge and Confinement of Quarks

In quantum chromodynamics with static quarks the confinement-deconfinement phase transition is connected to the spontaneous breaking of the global Z3 center symmetry. This symmetry is lost when one considers dynamical quarks. Owing to the fractional electric charge of quarks, we recover a global Z6 center symmetry when QCD is regarded as a part of the Standard Model. We present results from QCD-like theories extended by electromagnetic interactions and show that the weak coupling limit of the QED part of the model results in a center-like symmetry with disorder in the vacuum. This can be seen explicitly in a character expansion of the fermion determinant. Further, we show that corresponding center averages project the fermion determinant on N-ality zero and discuss whether the additional center symmetry can be used to eliminate the fermion sign problem in QCD with fundamental quarks.

hep-lat↗

arXiv2013

Hybrid Monte-Carlo simulation of interacting tight-binding model of graphene

In this work, results are presented of Hybrid-Monte-Carlo simulations of the tight-binding Hamiltonian of graphene, coupled to an instantaneous long-range two-body potential which is modeled by a Hubbard-Stratonovich auxiliary field. We present an investigation of the spontaneous breaking of the sublattice symmetry, which corresponds to a phase transition from a conducting to an insulating phase and which occurs when the effective fine-structure constant $α$ of the system crosses above a certain threshold $α_C$. Qualitative comparisons to earlier works on the subject (which used larger system sizes and higher statistics) are made and it is established that $α_C$ is of a plausible magnitude in our simulations. Also, we discuss differences between simulations using compact and non-compact variants of the Hubbard field and present a quantitative comparison of distinct discretization schemes of the Euclidean time-like dimension in the Fermion operator.

hep-lat↗

arXiv2013

$G_2$-QCD: Spectroscopy and the phase diagram at zero temperature and finite density

Due to the fermion sign problem, standard lattice Monte-Carlo method for QCD fail at small temperatures and high baryon densities. $G_2$-QCD, QCD with the gauge group $SU(3)$ replaced by the exceptional Lie group $G_2$, can be simulated using lattice techniques at these densities, and can therefore provide an illustration of the possible phase structure. Here we present a systematic investigation of the ground-state hadronic spectrum using lattice simulations for different quark masses in several hadronic sectors. We then show that the different hadronic scales of Goldstone bosons, intermediate bosons, and baryons is reflected in the phase structure at finite density.

hep-lat↗