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Christof Gattringer

Publications and source records attributed to Christof Gattringer.

At least 73 records · Page 4Linked to original sources
arXiv2014

New developments for dual methods in lattice field theory at non-zero density

In recent years the complex action problem of lattice field theory at finite density was overcome for several system by mapping them to dual variables (flux lines and surfaces). We illustrate this mapping for the case of the U(1) gauge Higgs system and present some representative physics results for this model. Conceptual challenges such as spectroscopy in the dual approach, as well as algorithmic developments are discussed and related ideas for systems with fermions are addressed. Models where the dual variables approach solves the complex action problem can serve as reference systems for other approaches to finite density lattice field theory and we discuss some examples. Finally we address the strategy of a partial dualization in certain limits, e.g., for strong coupling and large mass.

hep-lat↗
arXiv2013

Effective Lagrangian for the Polyakov line on a lattice

We formulate a method for computing the effective Lagrangian of the Polyakov line on the lattice. Using mean field approximation we calculate the effective potential for high temperatures. The result agrees with recent lattice simulations. We reveal a new type of ultraviolet divergence (coming from longitudinal gluons) which dominates the effective potential and explains the discrepancy of the lattice simulations and standard perturbative calculations performed in covariant gauges.

hep-lat↗
arXiv2013

Solving the sign problem of two flavor scalar electrodynamics at finite chemical potential

We explore two flavor scalar electrodynamics on the lattice, which has a complex phase problem at finite chemical potential. By rewriting the action in terms of dual variables this complex phase problem can be solved exactly. The dual variables are link- and plaquette occupation numbers, subject to local constraints that have to be respected by the Monte Carlo algorithm. For the simulation we use a local update as well as the newly developed "surface worm algorithm", which is a generalization of the Prokof'ev Svistunov worm algorithm concept for simulating the dual representation of abelian Gauge-Higgs models on a lattice. We assess the performance of the two algorithms, present results for the phase diagram and discuss condensation phenomena.

hep-lat↗
arXiv2013

Taylor- and fugacity expansion for the effective center model of QCD at finite density

Using the effective center model of QCD we test series expansions for finite chemical potential $μ$. In particular we study two variants of Taylor expansion as well as the fugacity series. The effective center model has a dual representation where the sign problem is absent and reliable Monte Carlo simulations are possible at arbitrary $μ$. We use the results from the dual simulation as reference data to assess the Taylor- and fugacity series approaches. We find that for most of parameter space fugacity expansion is the best (but also numerically most expensive) choice for reproducing the dual simulation results, while conventional Taylor expansion is reliable only for very small $μ$. We also discuss the results of a modified Taylor expansion in $e^{\pm μ} - 1 $ which at the same numerical effort clearly outperforms the conventional Taylor series.

hep-lat↗
arXiv2013

Local Polyakov loop domains and their fractality

We discuss properties of local Polyakov loops in the deconfinement transition of SU(3) lattice gauge theory at finite temperature using the fixed scale approach. In particular we study spatial clusters where local Polyakov loops have phases near the same center elements of the gauge group. We present results for various properties of the center clusters, e.g., their percolation probability or their fractality and discuss the physical implications for temperatures below and above the phase transition.

hep-lat↗
arXiv2013

Dual Methods for Lattice Field Theories at Finite Density

We present a dual representation of the partition function of the charged scalar field in which the complex action problem at non-zero chemical potential is absent. In this dual representation Monte Carlo simulations are possible and we show some physical results obtained with this approach. Furthermore we present a technique to study 2-point functions at finite density. Results for the lattice correlators at various chemical potentials are shown and discussed.

hep-lat↗
arXiv2013

Dual lattice simulation of the U(1) gauge-Higgs model at finite density - an exploratory proof-of-concept study

The U(1) gauge-Higgs model with two flavors of opposite charge and a chemical potential is mapped exactly to a dual representation where matter fields correspond to loops of flux and the gauge fields are represented by surfaces. The complex action problem of the conventional formulation at finite chemical potential mu is overcome in the dual representation and the partition sum has only real and non-zero contributions. We simulate the model in the dual representation using a generalized worm algorithm, explore the phase diagram and study condensation phenomena at finite mu.

hep-lat↗
arXiv2013

Surface worm algorithm for abelian Gauge-Higgs systems on the lattice

The Prokof'ev Svistunov worm algorithm was originally developed for models with nearest neighbor interactions that in a high temperature expansion are mapped to systems of closed loops. In this work we present the surface worm algorithm (SWA) which is a generalization of the worm algorithm concept to abelian Gauge-Higgs models on a lattice which can be mapped to systems of surfaces and loops (dual representation). Using Gauge-Higgs models with gauge groups Z(3) and U(1) we compare the SWA to the conventional approach and to a local update in the dual representation. For the Z(3) case we also consider finite chemical potential where the conventional representation has a sign problem which is overcome in the dual representation. For a wide range of parameters we find that the SWA clearly outperforms the local update.

hep-lat↗
arXiv2013

Spectroscopy in finite density lattice field theory: An exploratory study in the relativistic Bose gas

We analyze 2-point functions in the relativistic Bose gas on the lattice, i.e., a charged scalar phi-4 field with chemical potential mu. Using a generalized worm algorithm we perform a Monte Carlo simulation in a dual representation in terms of fluxes where the complex action problem is overcome. We explore various aspects of lattice spectroscopy at finite density and zero temperature, such as the asymmetry of forward and backward propagation in time and the transition into the condensed phase. It is shown that after a suitable subtraction the exponents for forward and backward propagation are independent of mu and agree with the mass obtained from the propagator at mu = 0. This holds for mu < mu_c and shows that below the condensation transition the mass is independent of mu as expected from the Silver Blaze scenario.

hep-lat↗
arXiv2012

Flux simulation of the SU(3) spin model at finite chemical potential

We present a Monte Carlo simulation of an effective theory for local Polyakov loops at finite temperature and density. The sign problem is overcome by mapping the partition sum to a flux representation. We determine the phase diagram of the model as a function of the temperature and the chemical potential.

hep-lat↗
arXiv2012

Monte Carlo simulation of abelian gauge-Higgs lattice models using dual representation

We study abelian gauge-Higgs models on the lattice and consider gauge groups Z(3) and U(1). For both cases the partition sums are mapped exactly to a dual representation where the degrees of freedom are surfaces for the gauge fields and loops of flux that may serve as boundaries for the surfaces represent the matter fields. Also at finite chemical potential the dual partition sums have only real and positive contributions and the complex action problem of the conventional representation is overcome in the dual approach. We apply a local Metropolis update for the dual degrees of freedom, as well as a generalization of the worm algorithm to bounded surfaces. Results that illustrate condensation phenomena as a function of chemical potential are discussed.

hep-lat↗
arXiv2012

Gauge and matter fields as surfaces and loops - an exploratory lattice study of the Z(3) Gauge-Higgs model

We discuss a representation of the Z(3) Gauge-Higgs lattice field theory at finite density in terms of dual variables, i.e., loops of flux and surfaces. In the dual representation the complex action problem of the conventional formulation is resolved and Monte Carlo simulations at arbitrary chemical potential become possible. A suitable algorithm based on plaquette occupation numbers and link-fluxes is introduced and we analyze the model at zero temperature and finite density both in the weak and strong coupling phases. We show that at zero temperature the model has different first order phase transitions as a function of the chemical potential both for the weak and strong coupling phases. The exploratory study demonstrates that alternative degrees of freedom may successfully be used for Monte Carlo simulations in several systems with gauge and matter fields.

hep-lat↗
arXiv2012

No coincidence of center percolation and deconfinement in SU(4) lattice gauge theory

We study the behavior of center sectors in pure SU(4) lattice gauge theory at finite temperature. The center sectors are defined as spatial clusters of neighboring sites with values of their local Polyakov loops near the same center elements. We study the connectedness and percolation properties of the center clusters across the deconfinement transition. We show that for SU(4) gauge theory deconfinement cannot be described as a percolation transition of center clusters, a finding which is different from pure SU(2) or pure SU(3) Yang Mills theory, where the percolation description even allows for a continuum limit.

hep-lat↗
arXiv2012

Properties of canonical determinants and a test of fugacity expansion for finite density lattice QCD with Wilson fermions

We analyze canonical determinants, i.e., grand canonical determinants projected to a fixed net quark number. The canonical determinants are the coefficients in a fugacity expansion of the grand canonical determinant and we evaluate them as the Fourier moments of the grand canonical determinant with respect to imaginary chemical potential, using a dimensional reduction technique. The analysis is done for two mass-degenerate flavors of Wilson fermions at several temperatures below and above the confinement/deconfinement crossover. We discuss various properties of the canonical determinants and analyse the convergence of the fugacity series for different temperatures.

hep-lat↗
arXiv2012

Worm algorithms for the 3-state Potts model with magnetic field and chemical potential

We discuss worm algorithms for the 3-state Potts model with external field and chemical potential. The complex phase problem of this system can be overcome by using a flux representation where the new degrees of freedom are dimer and monomer variables. Working with this representation we discuss two different generalizations of the conventional Prokof'ev-Svistunov algorithm suitable for Monte Carlo simulations of the model at arbitrary chemical potential and evaluate their performance.

hep-lat↗
arXiv2011

The QCD Phase Diagram with Effective Theories

We study two effective theories for QCD at non-zero temperature and finite chemical potential, using local Polyakov loops as the degrees of freedom. The sign problem is solved by exactly mapping the partition function to a sum over flux and monomer variables with only real and positive weights, making the two models accessible to Monte Carlo simulation techniques. We use generalized worm algorithms and a local Metropolis update to perform the simulations and determine the phase diagram as a function of the temperature and the chemical potential.

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