arXiv subjects
Publications and source records attributed to Christian Hoelbling.
We present an algorithm that addresses topological freezing in lattice QCD simulations by combining parallel tempering with collective-variable-based enhanced sampling methods, and apply it to a particularly challenging system with $N_f = 2$ staggered fermions. We find that the algorithm unfreezes the system, which is otherwise completely frozen for approximately 40000 Molecular Dynamics Units with the Rational Hybrid Monte Carlo algorithm.
We present numerical results of staggered fermions with a taste splitting mass term on dynamical configurations. The rise of gluonic counterterms from rotational symmetry breaking is studied for a single taste operator and the pion propagator is computed. Preliminary numerical results are given for lattice sizes up to 16^4.
In theories with topological sectors, such as lattice QCD and four-dimensional SU(N) gauge theories with periodic boundary conditions, conventional update algorithms suffer from topological freezing due to large action barriers separating distinct sectors. With appropriately constructed bias potentials, Metadynamics and related enhanced sampling techniques can mitigate this problem and significantly reduce the integrated autocorrelation times of the topological charge and associated observables. We test strategies to accelerate the buildup of bias potentials and the possibility of extrapolating potentials from small to large volumes. We also investigate the effectiveness of orthogonal algorithmic improvements, such as longer HMC trajectories and HMC variants, which may benefit conventional simulations as well.
When approaching the continuum limit in lattice QCD or other theories in a setup with topological sectors, conventional update algorithms experience a particularly severe form of critical slowing down that is caused by high action barriers between the sectors. The qualitative scaling behavior of this critical slowing down appears to be universal across different update algorithms and (gauge) actions. We demonstrate that a combination of Metadynamics with parallel tempering, along with other modifications, can significantly reduce autocorrelation times while avoiding the need for reweighting. We also discuss strategies to extend the methods to QCD simulations with dynamical fermions, and present first results for $N_f = 2$ simulations at unphysical pion masses.
We present analytical and numerical results on symmetry properties of staggered fermions with taste splitting mass terms. As staggered species split differently for different types of taste splitting masses, various lattice symmetry subgroups and symmetry properties emerge. From the breaking of rotational symmetry, gluonic counterterms emerge. Preliminary numerical results are given for lattice sizes up to $8^4$.
At fine lattice spacings, Markov chain Monte Carlo simulations of QCD and other gauge theories with or without fermions are plagued by slow modes that give rise to large autocorrelation times. This can lead to simulation runs that are effectively stuck in one topological sector, a problem known as topological freezing. Here, we demonstrate that for a relevant set of parameters, Metadynamics can be used to unfreeze 4-dimensional SU(3) gauge theory. However, compared to local update algorithms and the Hybrid Monte Carlo algorithm, the computational overhead is significant in pure gauge theory, and the required reweighting procedure may considerably reduce the effective sample size. To deal with the latter problem, we propose modifications to the Metadynamics bias potential and the combination of Metadynamics with parallel tempering. We test the new algorithm in 4-dimensional SU(3) gauge theory and find that it can achieve topological unfreezing without compromising the effective sample size, thereby reducing the autocorrelation times of topological observables by at least two orders of magnitude compared to conventional update algorithms. Additionally, we observe significantly improved scaling of autocorrelation times with the lattice spacing in 2-dimensional U(1) gauge theory.
The automatic fine-tuning of isospin breaking effects by conformal coalescence found by Georgi in the 2-flavor Schwinger model is studied. The analytical results obtained for the bosonic correlators are elaborated and the mass splitting parameter in leading order determined. Numerical investigation of meson mass splitting confirms the exponential suppression of symmetry breaking effects even for mass differences $δm$ near the fermion mass $m_f$.
At fine lattice spacings, lattice simulations are plagued by slow (topological) modes that give rise to large autocorrelation times. These, in turn, lead to statistical and systematic errors that are difficult to estimate. We study the problem and possible algorithmic solutions in 4-dimensional SU(3) gauge theory, with special focus on instanton updates and Metadynamics.
Topological freezing is a well known problem in lattice simulations: with shrinking lattice spacing a transition between topological sectors becomes increasingly improbable, leading to a problematic increase of the autocorrelation time regarding several observables. We present our investigation of metadynamics as a solution for topological freezing in the Schwinger model. Specifically, we take a closer look at the collective variable and its scaling behaviour, visualize the effects of topological freezing and how metadynamics helps in that respect and explore alternatives for a more efficient building process. Possible implications for and differences to four-dimensional SU(3) theory are briefly discussed.
We give an explicit proof for the locality of staggered overlap operators. The proof covers the original two flavor construction by Adams as well as a single flavor version. As in the case of Neuberger's operator, an admissibility condition for the gauge fields is required.
We present a method to study the semiclassical gravitational collapse of a radially symmetric scalar quantum field in a coherent initial state. The formalism utilizes a Fock space basis in the initial metric, is unitary and time reversal invariant up to numerical precision. It maintains exact compatibility of the metric with the expectation values of the energy momentum tensor in the scalar field coherent state throughout the entire time evolution. We find a simple criterion for the smallness of discretization effects, which is violated when a horizon forms. As a first example, we study the collapse of a specific state in the angular momentum $l=0$ approximation. Outside the simulated volume it produces a Schwarzschild metric with $r_s \sim 3.5 \ell_p$. We see behaviour that is compatible with the onset of horizon formation both in the semiclassical and corresponding classical cases in a regime where we see no evidence for large discretization artefacts. In our example setting, we see that quantum effects accelerate the possible horizon formation and move it radially outward. We find that this effect is robust against variations of the radial resolution, the time step, the volume, the initial position and shape of the inmoving state, the vacuum subtraction, the discretization of the time evolution operator and the integration scheme of the metric. We briefly discuss potential improvements of the method and the possibility of applying it to black hole evaporation. We also briefly touch on the extension of our formalism to higher angular momenta, but leave the details and numerics for a forthcoming publication.
In modern lattice simulations, conventional update algorithms do not allow for tunneling between topological sectors at fine lattice spacings. We compare the viability of multiple less commonly used algorithms (metadynamics, instanton updates, and multiscale thermalization) with respect to proper sampling of all topological sectors in the Schwinger model. We briefly comment on the prospects of applying these methods to 4-dimensional SU(3) simulations.
We present a new formalism for numerically treating the semiclassical gravitational collapse of a scalar quantum field in the radially symmetric case. Our formalism is time reversal invariant and the evolution of the scalar fields is unitary. We present some first results in the angular momentum $l=0$ approximation for an initially coherent state of a massless field and briefly discuss future prospects.
We present a calculation of the leptonic decay-constant ratio $f_K/f_π$ in 2+1 flavor QCD. Our data set includes five lattice spacings and pion masses reaching down below the physical one. Special emphasis is placed on a careful study of all systematic uncertainties, especially the continuum extrapolation. Our result is perfectly compatible with the first-row unitarity constraint of the Standard Model.
We construct domain wall fermions with a staggered kernel and investigate their spectral and chiral properties numerically in the Schwinger model. In some relevant cases we see an improvement of chirality by more than an order of magnitude as compared to usual domain wall fermions. Moreover, we present first results for four-dimensional quantum chromodynamics, where we also observe significant reductions of chiral symmetry violations for staggered domain wall fermions.
We follow up on a suggestion by Adams and construct explicit domain wall fermion operators with staggered kernels. We compare different domain wall formulations, namely the standard construction as well as Borici's modified and Chiu's optimal construction, utilizing both Wilson and staggered kernels. In the process, we generalize the staggered kernels to arbitrary even dimensions and introduce both truncated and optimal staggered domain wall fermions. Some numerical investigations are carried out in the (1+1)-dimensional setting of the Schwinger model, where we explore spectral properties of the bulk, effective and overlap Dirac operators in the free-field case, on quenched thermalized gauge configurations and on smooth topological configurations. We compare different formulations using the effective mass, deviations from normality and violations of the Ginsparg-Wilson relation as measures of chirality.
We present preliminary results of a 2+1-flavor study of finite-volume effects in the lattice QCD computation of the leading-order hadronic contribution to the muon anomalous magnetic moment. We also present methods for obtaining directly the invariant hadronic polarization function, $Π(Q^2)$, and the Adler function at all discrete lattice values of $Q^2$, including $Q^2=0$. Results are obtained with HEX-smeared clover fermions.
We report on a continuum extrapolated result (arXiv:1309.5258) for the equation of state (EoS) of QCD with $N_f=2+1$ dynamical quark flavors and discuss preliminary results obtained with an additional dynamical charm quark ($N_f=2+1+1$). For all our final results, the systematics are controlled, quark masses are set to their physical values, and the continuum limit is taken using at least three lattice spacings corresponding to temporal extents up to $N_t=16$.