arXiv subjects

Lorenz von Smekal

Publications and source records attributed to Lorenz von Smekal.

At least 91 records · Page 5Linked to original sources

arXiv2013

On two- and three-point functions of Landau gauge Yang-Mills theory

We present results for the gluon and ghost propagators and the ghost-gluon vertex obtained from Dyson-Schwinger equations. In the zero temperature case we elaborate on the role of the three-gluon vertex and discuss a model that can capture its qualitative features like its anomalous dimensions and a zero crossing of the dressing function. Our results compare well with lattice data. At non-zero temperature we calculated the ghost propagator which agrees rather well with lattice results already within our simple truncation. These results are used to obtain the temperature dependence of the ghost-gluon vertex. We also explain why the ghost propagator does not react to the phase transition despite its direct coupling to the chromoelectric gluon.

hep-lat↗

arXiv2013

Effective potential for SU(2) Polyakov loops and Wilson loop eigenvalues

We simulate SU(2) gauge theory at temperatures ranging from slightly below $T_c$ to roughly $2T_c$ for two different values of the gauge coupling. Using a histogram method, we extract the effective potential for the Polyakov loop and for the phases of the eigenvalues of the thermal Wilson loop, in both the fundamental and adjoint representations. We show that the classical potential of the fundamental loop can be parametrized within a simple model which includes a Vandermonde potential and terms linear and quadratic in the Polyakov loop. We discuss how parametrizations for the other cases can be obtained from this model.

hep-lat↗

arXiv2013

On the influence of three-point functions on the propagators of Landau gauge Yang-Mills theory

We solve the Dyson-Schwinger equations of the ghost and gluon propagators of Landau gauge Yang-Mills theory together with that of the ghost-gluon vertex. The latter plays a central role in many truncation schemes for functional equations. By including it dynamically we can determine its influence on the propagators. We also suggest a new model for the three-gluon vertex motivated by lattice data which plays a crucial role to obtain stable solutions when the ghost-gluon vertex is included. We find that both vertices have a sizable quantitative impact on the mid-momentum regime and contribute to the reduction of the gap between lattice and Dyson-Schwinger equation results. Furthermore, we establish that the three-gluon vertex dressing turns negative at low momenta as suggested by lattice results in three dimensions.

hep-th↗

arXiv2013

Lattice BRST without Neuberger 0/0 problem

We illustrate in a simple toy model how the methods of SUSY quantum mechanics and topological quantum field theory can be used for covariant gauge-fixing with unbroken BRST symmetry on a finite lattice.

hep-th↗

arXiv2013

Going beyond the propagators of Landau gauge Yang-Mills theory

We present results for the propagators and the ghost-gluon vertex of Landau gauge Yang-Mills theory obtained from Dyson-Schwinger equations. Solving these three quantities simultaneously constitutes a new step in truncating these equations. We also introduce a new model for the three-gluon vertex that is motivated by lattice results. It features a zero crossing which is confirmed a posteriori by a Dyson-Schwinger calculation. Within our setup we can reproduce lattice data very well. We establish that also for the ghost-gluon vertex a difference between decoupling and scaling solutions is present. For the scaling solution we discuss the possibility of modifying the infrared exponents via an angle dependence of the ghost-gluon vertex. However, no such dependence is found in our calculations. Finally, we calculate the Schwinger function for the gluon propagator.

hep-th↗

arXiv2012

Fluctuations in the quark-meson model for QCD with isospin chemical potential

We study the two-flavor quark-meson (QM) model with the functional renormalization group (FRG) to describe the effects of collective mesonic fluctuations on the phase diagram of QCD at finite baryon and isospin chemical potentials, $μ_B$ and $μ_I$. With only isospin chemical potential there is a precise equivalence between the competing dynamics of chiral versus pion condensation and that of collective mesonic and baryonic fluctuations in the quark-meson-diquark model for two-color QCD at finite baryon chemical potential. Here, finite $μ_B=3μ$ introduces an additional dimension to the phase diagram as compared to two-color QCD, however. At zero temperature, the ($μ_I,μ$)-plane of this phase diagram is strongly constrained by the "Silver Blaze problem." In particular, the onset of pion condensation must occur at $μ_I= m_π/2$, independent of $μ$ as long as $μ+ μ_I$ stays below the constituent quark mass of the QM model or the liquid-gas transition line of nuclear matter in QCD. In order to maintain this relation beyond mean field it is crucial to compute the pion mass from its timelike correlator with the FRG in a consistent way.

hep-ph↗

arXiv2012

Determination of LambdaMS from the gluon and ghost propagators in Landau gauge

We give an update on our lattice determination of r_0 LambdaMS for different Nf. Our calculations employ the strong coupling constant in the minimal MOM scheme for QCD in Landau gauge, and we report here on our progress towards a quantitative understanding of the intrinsic lattice discretization artifacts at large momenta. This is important for a high-precision analysis, in particular for the unquenched calculations for which the access to small lattice spacings is restricted by the available gauge configurations.

hep-lat↗

arXiv2012

Two- and three-point functions in two-dimensional Landau-gauge Yang-Mills theory: Continuum results

We investigate the Dyson-Schwinger equations for the gluon and ghost propagators and the ghost-gluon vertex of Landau-gauge gluodynamics in two dimensions. While this simplifies some aspects of the calculations as compared to three and four dimensions, new complications arise due to a mixing of different momentum regimes. As a result, the solutions for the propagators are more sensitive to changes in the three-point functions and the ansaetze used for them at the leading order in a vertex a expansion. Here, we therefore go beyond this common truncation by including the ghost-gluon vertex self-consistently for the first time, while using a model for the three-gluon vertex which reproduces the known infrared asymptotics and the zeros at intermediate momenta as observed on the lattice. A separate computation of the three-gluon vertex from the results is used to confirm the stability of this behavior a posteriori. We also present further arguments for the absence of the decoupling solution in two dimensions. Finally, we show how in general the infrared exponent kappa of the scaling solutions in two, three and four dimensions can be changed by allowing an angle dependence and thus an essential singularity of the ghost-gluon vertex in the infrared.

hep-th↗

arXiv2012

The phase diagram of a gauge theory with fermionic baryons

The fermion-sign problem at finite density is a persisting challenge for Monte-Carlo simulations. Theories that do not have a sign problem can provide valuable guidance and insight for physically more relevant ones that do. Replacing the gauge group SU(3) of QCD by the exceptional group G2, for example, leads to such a theory. It has mesons as well as bosonic and fermionic baryons, and shares many features with QCD. This makes the G2 gauge theory ideally suited to study general properties of dense, strongly-interacting matter, including baryonic and nuclear Fermi pressure effects. Here we present the first-ever results from lattice simulations of G2 QCD with dynamical fermions, providing a first explorative look at the phase diagram of this QCD-like theory at finite temperature and baryon chemical potential.

hep-lat↗

arXiv2012

Universal Aspects of QCD-like Theories

In these lectures I review some basic examples of how the concepts of universality and scaling can be used to study aspects of the chiral and the deconfinement transition, if not in QCD directly but in QCD-like theories. As an example for flavor dynamics I discuss a quark-hadron model to describe the phase diagram of two-color QCD with the functional renormalization group. Universal aspects of deconfinement are illustrated mainly in the 2+1 dimensional SU(N) gauge theories with second order transition where many exact results from spin models can be exploited.

hep-ph↗

arXiv2012

The gluon propagator close to criticality

The deconfinement phase transition of pure Yang-Mills theory at finite temperature is reflected in the behavior of gauge-fixed gluonic correlation functions. This is one of many examples of how physical information can be extracted from gauge-dependent correlations which is not always obvious. Here, we study the behavior of the Landau-gauge gluon propagator of pure SU(2) across the phase transition in 2+1 and 3+1 dimensions in order to assess to what extend the corresponding critical behavior is reflected in these correlations. We discuss why it should emerge from a continuum perspective and test our expectations in lattice simulations. A comparison with SU(3) furthermore reveals quite clear indications for a sensitivity of the gluon propagator to the order of the transition.

hep-lat↗

arXiv2012

Quark-meson-diquark model for two-color QCD

We introduce a two-flavor quark-meson-diquark model for two-color QCD and its extensions to include gauge-field dynamics as described by the Polakov loop. Grand potential and phase structure are being studied both in mean-field approximation and with the functional renormalization group. The model provides an explicit example for the importance of baryonic degrees of freedom: When they are omitted, the phase diagram closely resembles that of the corresponding (Polyakov)-quark-meson models for QCD, in particular including their critical endpoint. In order to reproduce the well established main features based on the symmetries and breaking patterns of two-color QCD, however, they must be included and there is no critical endpoint. The competing dynamics of collective mesonic and baryonic fluctuations is well described by the functional renormalization group equation in lowest order derivative expansion for the effective potential which we solve numerically on a two-dimensional grid in field space.

hep-ph↗

arXiv2012

Fractional electric charge and quark confinement

Owing to their fractional electric charges, quarks are blind to transformations that combine a color center phase with an appropriate electromagnetic one. Such transformations are part of a global $Z_6$-like center symmetry of the Standard Model that is lost when quantum chromodynamics (QCD) is treated as an isolated theory. This symmetry and the corresponding topological defects may be relevant to non-perturbative phenomena such as quark confinement, much like center symmetry and ordinary center vortices are in pure SU($N$) gauge theories. Here we report on our investigations of an analogous symmetry in a 2-color model with dynamical Wilson quarks carrying half-integer electric charge.

hep-lat↗

arXiv2012

An improved formalism for the Grover search algorithm

The Grover search algorithm is one of the two key algorithms in the field of quantum computing, and hence it is of significant interest to describe it in the most efficient mathematical formalism. We show firstly, that Clifford's formalism of geometric algebra, provides a significantly more efficient representation than the conventional Bra-ket notation, and secondly, that the basis defined by the states of maximum and minimum weight in the Grover search space, allows a simple visualization of the Grover search as the precession of a spin-1/2 particle. Using this formalism we efficiently solve the exact search problem, as well as easily representing more general search situations.

quant-ph↗

arXiv2011

A Precise Error Bound for Quantum Phase Estimation

Quantum phase estimation is one of the key algorithms in the field of quantum computing, but up until now, only approximate expressions have been derived for the probability of error. We revisit these derivations, and find that by ensuring symmetry in the error definitions, an exact formula can be found. This new approach may also have value in solving other related problems in quantum computing, where an expected error is calculated. Expressions for two special cases of the formula are also developed, in the limit as the number of qubits in the quantum computer approaches infinity and in the limit as the extra added qubits to improve reliability goes to infinity. It is found that this formula is useful in validating computer simulations of the phase estimation procedure and in avoiding the overestimation of the number of qubits required in order to achieve a given reliability. This formula thus brings improved precision in the design of quantum computers.

quant-ph↗

arXiv2010

Universal Aspects of Deconfinement in 2+1 Dimensions

The 2+1 dimensional pure SU(N) gauge theories with N <= 4 are candidates for applying the powerful tools of scaling and universality to their deconfinement transitions at finite temperature. The corresponding 2 dimensional q-state Potts models with q <= 4 have 2nd order transitions, and we can exploit many exact results to obtain accurate critical couplings, transition temperatures, critical exponents, and the leading behavior of the continuum string tension near the phase transition on one side, together with its dual on the other. Thereby, the self-duality of the 2d spin models is reflected in a duality between spacelike vortices and confining electric fluxes. We also discuss the relevance of center symmetry and the corresponding vortices for confinement in full QCD when the electromagnetic interactions of fractionally charged quarks are included.

hep-ph↗

arXiv2010

SU(3) Deconfinement in (2+1)d from Twisted Boundary Conditions and Self-Duality

We study the pure SU(3) gauge theory in 2+1 dimensions on the lattice using 't Hooft's twisted boundary conditions to force non-vanishing center flux through the finite volume. In this way we measure the free energy of spacelike center vortices as an order parameter for the deconfinement transition. The transition is of 2nd order in the universality class of the 2d 3-state Potts model, which is self-dual. This self-duality can be observed directly in the SU(3) gauge theory, and it can be exploited to extract critical couplings with high precision in rather small volumes. We furthermore obtain estimates for critical exponents and the critical temperature in units of the dimensionful continuum coupling. Finally, we also apply our methods to the (2+1)d SU(4) gauge theory which was previously found to have a weak 1st order transition. We nevertheless observe at least approximate q = 4 Potts scaling at length scales corresponding to the lattice sizes used in our simulations.

hep-lat↗

arXiv2010

Exploring a hidden symmetry with electrically charged quarks

It is usual to study confinement via quantum chromodynamics (QCD) alone. The deconfinement transition of the pure gauge theory (i.e. with static quarks) is then characterized by the breaking of center symmetry. Center vortices offer an intuitive and quantitative description of the transition. Dynamical quarks explicitly break center symmetry, and the phase transition becomes a crossover. However, it may be misleading to study QCD in isolation. Quarks also carry fractional electric charge. This bestows the Standard Model with a global center symmetry that combines color center phases with an appropriate electromagnetic phase. Is this symmetry relevant to confinement? We begin our investigation by studying a 2-color model of QCD with half-integer electrically charged quarks.

hep-lat↗