arXiv subjects

Falk Bruckmann

Publications and source records attributed to Falk Bruckmann.

At least 37 records · Page 2Linked to original sources

arXiv2013

Subset method for one-dimensional QCD

We present a subset method which solves the sign problem for QCD at nonzero quark chemical potential in 0+1 dimensions. The subsets gather gauge configurations based on the center symmetry of the SU(3) group. We show that the sign problem is solved for one to five quark flavors and that it slowly reappears for a larger number of flavors. We formulate an extension of the center subsets that solves the sign problem for a larger number of flavors as well. We also derive some new analytical results for this toy model.

hep-lat↗

arXiv2013

Blocking-inspired supersymmetric actions: a status report

We provide a status report on the advances in blocking-inspired supersymmetric actions. This is done at the example of interacting supersymmetric quantum mechanics as well as the Wess-Zumino model. We investigate in particular the implications of a nontrivial realisation of translational symmetry on the lattice in this approach. We also discuss the locality of symmetry generators.

hep-lat↗

arXiv2013

Topological zero modes at nonzero chemical potential

We give analytical and numerical solutions for the zero modes of the Dirac operator in topological SU(2) gauge backgrounds at nonzero chemical potential. Continuation from imaginary to real chemical potential is used to systematically derive analytical zero modes for calorons at arbitrary holonomy and, in particular limits, for instantons and dyons (magnetic monopoles). For the latter a spherical ansatz is explored as well. All the zero mode exhibit stronger peaks at the core and negative regions in their densities. We discuss the structure of the corresponding overlap matrix elements. For discretized calorons on the lattice we consider the staggered operator and show that it does possess (quartet quasi-)zero modes, whose eigenmodes agree very well with the continuum profiles, also for nonzero chemical potential.

hep-ph↗

arXiv2012

Application of Ewald's Method for Efficient Summation of Dyon Long-Range Potentials

We study a model of dyons for SU(2) Yang-Mills theory at finite temperature T < T_c, in particular its ability to generate a confining force between a static quark antiquark pair. The interaction between dyons corresponds to a long-range 1/r potential, which in naive treatments with a finite number of dyons typically gives rise to severe finite volume effects. To avoid such effects we apply the so-called Ewald method, which has its origin in solid state physics. The basic idea of Ewald's method is to consider a finite number of dyons inside a finite cubic volume and enforce periodicity of this volume. We explain the technicalities of Ewald's method and outline how the method can be applied to a wider class of 1/r^p long-range potentials.

hep-ph↗

arXiv2012

Subsets and the canonical partition functions

We explain the physical nature of the subset solution to the sign problem in chiral random matrix theory: The subset sum is shown to project out the canonical determinant with zero quark charge from a given configuration. As the grand canonical chiral random matrix partition function is independent of the chemical potential, the zero quark charge sector provides the full result.

hep-lat↗

arXiv2012

Improved lattice actions for supersymmetric quantum mechanics

We analyze the Euclidean version of supersymmetric quantum mechanics on the lattice by means of a numerical path integral. We consider two different lattice derivatives and improve the actions containing them with respect to supersymmetry by systematically adding interaction terms with non-zero extent. To quantize this improvement, we measure boson and fermion masses and Ward identities for the naive as well as the improved models. The masses are degenerate in all models, but the magnitude of the Ward identities decreases significantly for both derivative operators using the improved actions. This is a clear sign that the breaking of supersymmetry due to lattice artifacts is reduced.

hep-lat↗

arXiv2012

Level spacings for weakly asymmetric real random matrices and application to two-color QCD with chemical potential

We consider antisymmetric perturbations of real symmetric matrices in the context of random matrix theory and two-color quantum chromodynamics. We investigate the level spacing distributions of eigenvalues that remain real or become complex conjugate pairs under the perturbation. We work out analytical surmises from small matrices and show that they describe the level spacings of large random matrices. As expected from symmetry arguments, these level spacings also apply to the overlap Dirac operator for two-color QCD with chemical potential.

hep-lat↗

arXiv2012

Wigner surmise for mixed symmetry classes in random matrix theory

We consider the nearest-neighbor spacing distributions of mixed random matrix ensembles interpolating between different symmetry classes, or between integrable and non-integrable systems. We derive analytical formulas for the spacing distributions of 2x2 or 4x4 matrices and show numerically that they provide very good approximations for those of random matrices with large dimension. This generalizes the Wigner surmise, which is valid for pure ensembles that are recovered as limits of the mixed ensembles. We show how the coupling parameters of small and large matrices must be matched depending on the local eigenvalue density.

math-ph↗

arXiv2012

Confining dyon gas with finite-volume effects under control

As an approach to describe the long-range properties of non-Abelian gauge theories at non-zero temperature T < T_c, we consider a non-interacting ensemble of dyons (magnetic monopoles) with non-trivial holonomy. We show analytically, that the quark-antiquark free energy from the Polyakov loop correlator grows linearly with the distance, and how the string tension scales with the dyon density. In numerical treatments, the long-range tails of the dyon fields cause severe finite-volume effects. Therefore, we demonstrate the application of Ewald's summation method to this system. Finite-volume effects are shown to be under control, which is a crucial requirement for numerical studies of interacting dyon ensembles.

hep-ph↗

arXiv2012

Topology of dynamical lattice configurations including results from dynamical overlap fermions

We investigate how the topological charge density in lattice QCD simulations is affected by violations of chiral symmetry caused by the fermion action. To this end we compare lattice configurations generated with a number of different actions including first configurations generated with exact dynamical overlap quarks. We visualize the topological profiles after mild smearing. In the topological charge correlator we measure the size of the positive core, which is known to shrink to zero extension in the continuum limit. To leading order we find the core size to scale linearly with the lattice spacing with the same coefficient for all actions, even including quenched simulations. In the subleading term the different actions vary over a range of about 10 %. Our findings suggest that non-chiral lattice actions at current lattice spacings do not differ much for observables related to topology, both among themselves and compared to overlap fermions.

hep-lat↗

arXiv2011

High temperature quark localization by Polyakov loops

We study the low eigenmodes of the overlap and staggered Dirac operator at high temperature. We show that the recently found localized quark modes obeying Poisson statistics are connected to physical gauge field objects with their size and density scaling in the continuum limit. The localized modes are also strongly correlated with large fluctuations of the Polyakov loop. Based on that we construct a random matrix model of the low Dirac modes inspired by dimensional reduction. Our model reproduces the Poisson to random matrix transition seen in the lattice Dirac spectrum.

hep-lat↗

arXiv2011

Dressed Wilson loops as dual condensates in response to magnetic fields

We introduce dressed Wilson loops as a novel confinement observable. It consists of closed planar loops of arbitrary geometry but fixed area and its expectation values decay with the latter. The construction of dressed Wilson loops is based on chiral condensates in response to magnetic (and electric) fields, thus linking different physical concepts. We present results for generalized condensates and dressed Wilson loops on dynamical lattice configurations and confirm the agreement with conventional Wilson loops in the limit of large probe mass. We comment on the renormalization of dressed Wilson loops.

hep-lat↗

arXiv2011

Topology of dynamical lattice configurations including results from dynamical overlap fermions

We investigate how the topological charge density in lattice QCD simulations is affected by violations of chiral symmetry in different fermion actions. To this end we compare lattice configurations generated with a number of different actions including first configurations generated with exact overlap quarks. We visualize the topological profiles after mild smearing. In the topological charge correlator we measure the size of the positive core, which is known to vanish in the continuum limit. To leading order we find the core size to scale linearly with the lattice spacing with the same coefficient for all actions, even including quenched simulations. In the subleading term the different actions vary over a range of about 10 %. Our findings suggest that non-chiral lattice actions at current lattice spacings do not differ much for this specific observable related to topology, both among themselves and compared to overlap fermions.

hep-lat↗

arXiv2011

Dressed Wilson loops as dual condensates in response to magnetic and electric fields

We introduce dressed Wilson loops as a novel confinement observable. It consists of closed planar loops of arbitrary geometry but fixed area, and its expectation values decay with the latter. The construction of dressed Wilson loops is based on chiral condensates in response to magnetic and electric fields, thus linking different physical concepts. We present results for generalized condensates and dressed Wilson loops on dynamical lattice configurations and confirm the agreement with conventional Wilson loops in the limit of large probe mass. We comment on the renormalization of dressed Wilson loops.

hep-lat↗

arXiv2011

Anderson localization through Polyakov loops: lattice evidence and Random matrix model

We investigate low-lying fermion modes in SU(2) gauge theory at temperatures above the phase transition. Both staggered and overlap spectra reveal transitions from chaotic (random matrix) to integrable (Poissonian) behavior accompanied by an increasing localization of the eigenmodes. We show that the latter are trapped by local Polyakov loop fluctuations. Islands of such "wrong" Polyakov loops can therefore be viewed as defects leading to Anderson localization in gauge theories. We find strong similarities in the spatial profile of these localized staggered and overlap eigenmodes. We discuss possible interpretations of this finding and present a sparse random matrix model that reproduces these features.

hep-lat↗

arXiv2010

Dual condensate and QCD phase transition

The dual condensate is a new QCD phase transition order parameter, which connnects confinement and chiral symmetry breaking as different mass limits. We discuss the relation between the fermion spectrum at general boundary conditions and the dual condensate and show numerical results for the latter from unquenched SU(3) lattice configurations.

hep-lat↗

arXiv2010

Vortex content of calorons and deconfinement mechanism

We reveal the center vortex content of SU(2) calorons and ensembles of them. While one part of the vortex connects the constituent dyons of a single caloron, another part is predominantly spatial and can be related to the twist that exists in the caloron gauge field. The latter part depends strongly on the caloron holonomy and degenerates to a plane between the dyons when the asymptotic Polyakov loop is traceless. Correspondingly, the spatial vortex in caloron ensembles is percolating in this case. This finding fits perfectly in the confinement scenario of vortices and shows that calorons are suitable to facilitate the vortex (de)confinement mechanism.

hep-th↗

arXiv2010

A random matrix-like model for the Polyakov loop and center symmetry

We formulate a random matrix-like model for the Polyakov loop in SU(N) Yang-Mills theories. It describes a simplified dynamics in terms of eigenvalue differences. The deconfinement phase transition encoded in center symmetry breaking is reproduced including its nature being first order for SU(3) and second order for SU(2). Analytical arguments about the phases are presented and a comparison to other approaches is made.

hep-ph↗