arXiv subjects

Karl Jansen

Publications and source records attributed to Karl Jansen.

At least 163 records · Page 9Linked to original sources

arXiv2020

Comparison of topological charge definitions in Lattice QCD

In this paper, we show a comparison of different definitions of the topological charge on the lattice. We concentrate on one small-volume ensemble with 2 flavours of dynamical, maximally twisted mass fermions and use three more ensembles to analyze the approach to the continuum limit. We investigate several fermionic and gluonic definitions. The former include the index of the overlap Dirac operator, the spectral flow of the Wilson--Dirac operator and the spectral projectors. For the latter, we take into account different discretizations of the topological charge operator and various smoothing schemes to filter out ultraviolet fluctuations: the gradient flow, stout smearing, APE smearing, HYP smearing and cooling. We show that it is possible to perturbatively match different smoothing schemes and provide a well-defined smoothing scale. We relate the smoothing parameters for cooling, stout and APE smearing to the gradient flow time $τ$. In the case of hypercubic smearing the matching is performed numerically. We investigate which conditions have to be met to obtain a valid definition of the topological charge and susceptibility and we argue that all valid definitions are highly correlated and allow good control over topology on the lattice.

hep-lat↗

arXiv2020

Improvement, generalization, and scheme conversion of Wilson-line operators on the lattice in the auxiliary field approach

Nonlocal quark bilinear operators connected by link paths are used for studying parton distribution functions (PDFs) and transverse momentum-dependent PDFs of hadrons using lattice QCD. The nonlocality makes it difficult to understand the renormalization and improvement of these operators using standard methods. In previous work, we showed that by introducing an auxiliary field on the lattice, one can understand an on-axis Wilson-line operator as the product of two local operators in an extended theory. In this paper, we provide details about the calculation in perturbation theory of the factor for conversion from our lattice-suitable renormalization scheme to the MS-bar scheme. Extending our work, we study Symanzik improvement of the extended theory to understand the pattern of discretization effects linear in the lattice spacing, $a$, which are present even if the lattice fermion action exactly preserves chiral symmetry. This provides a prospect for an eventual $O(a)$ improvement of lattice calculations of PDFs. We also generalize our approach to apply to Wilson lines along lattice diagonals and to piecewise-straight link paths.

hep-lat↗

arXiv2020

Topological vacuum structure of the Schwinger model with matrix product states

We numerically study the single-flavor Schwinger model with a topological $θ$-term, which is practically inaccessible by standard lattice Monte Carlo simulations due to the sign problem. By using numerical methods based on tensor networks, especially the one-dimensional matrix product states, we explore the non-trivial $θ$-dependence of several lattice and continuum quantities in the Hamiltonian formulation. In particular, we compute the ground-state energy, the electric field, the chiral fermion condensate, and the topological vacuum susceptibility for positive, zero, and even negative fermion mass. In the chiral limit, we demonstrate that the continuum model becomes independent of the vacuum angle $θ$, thus respecting CP invariance, while lattice artifacts still depend on $θ$. We also confirm that negative masses can be mapped to positive masses by shifting $θ\rightarrow θ+π$ due to the axial anomaly in the continuum, while lattice artifacts non-trivially distort this mapping. This mass regime is particularly interesting for the (3+1)-dimensional QCD analog of the Schwinger model, the sign problem of which requires the development and testing of new numerical techniques beyond the conventional Monte Carlo approach.

hep-lat↗

arXiv2020

Avoiding the sign-problem in lattice field theory

In lattice field theory, the interactions of elementary particles can be computed via high-dimensional integrals. Markov-chain Monte Carlo (MCMC) methods based on importance sampling are normally efficient to solve most of these integrals. But these methods give large errors for oscillatory integrands, exhibiting the so-called sign-problem. We developed new quadrature rules using the symmetry of the considered systems to avoid the sign-problem in physical one-dimensional models for the resulting high-dimensional integrals. This article gives a short introduction to integrals used in lattice QCD where the interactions of gluon and quark elementary particles are investigated, explains the alternative integration methods we developed and shows results of applying them to models with one physical dimension. The new quadrature rules avoid the sign-problem and can therefore be used to perform simulations at until now not reachable regions in parameter space, where the MCMC errors are too big for affordable sample sizes. However, it is still a challenge to develop these techniques further for applications with physical higher-dimensional systems.

hep-lat↗

arXiv2019

Zeta-regularized vacuum expectation values from quantum computing simulations

The zeta-regularization allows to establish a connection between Feynman's path integral and Fourier integral operator zeta-functions. This fact can be utilized to perform the regularization of the vacuum expectation values in quantum field theories. In this proceeding, we will describe the concept of the zeta-regularization, give a simple example and demonstrate that quantum computing can be employed to numerically evaluate zeta-regulated vacuum expectation values on a quantum computer.

hep-lat↗

arXiv2019

Quasi-PDFs with twisted mass fermions

We discuss the recent progress in extracting partonic functions from the quasi-distribution approach, using twisted mass fermions. This concerns, among others, the investigation of several sources of systematic effects. Their careful analysis is a prerequisite to obtain precise determinations of PDFs from the lattice with realistic estimates of all uncertainties. In these proceedings, we shortly discuss systematic effects in the matching procedure. Moreover, we present preliminary results from our new simulations at the physical point. They involve, additionally, the dynamical strange and charm quarks, as well as a larger volume and a smaller lattice spacing than in our previous computations. In addition, we show first results from computations of generalized parton distributions (GPDs) in the quasi-distribution framework.

hep-lat↗

arXiv2019

Zeta-regularized vacuum expectation values

It has recently been shown that vacuum expectation values and Feynman path integrals can be regularized using Fourier integral operator $ζ$-function, yet the physical meaning of these $ζ$-regularized objects was unknown. Here we show that $ζ$-regularized vacuum expectations appear as continuum limits using a certain discretization scheme. Furthermore, we study the rate of convergence for the discretization scheme using the example of a one-dimensional hydrogen atom in $(-π,π)$ which we evaluate classically, using the Rigetti Quantum Virtual Machine, and on the Rigetti 8Q quantum chip "Agave" device. We also provide the free radiation field as an example for the computation of $ζ$-regularized vacuum expectation values in a gauge theory.

quant-ph↗

arXiv2019

Parton distribution functions of $Δ^+$ on the lattice

We present results for renormalized matrix elements related to the unpolarized quasi-distribution function of the $Δ^+$ baryon making use of the large momentum effective theory. Two ensembles of $N_f=2+1+1$ twisted mass fermions with a clover term and pion masses of 250 MeV and 330 MeV are analyzed. We employ momentum smearing to improve the overlap with the boosted $Δ$ state significantly reducing in this way the statistical error of both two- and three-point functions.

hep-lat↗

arXiv2019

Investigating volume effects for N$_f$=2 twisted clover fermions at the physical point

In this work we present preliminary results on the nucleon axial and tensor charges, the quark momentum fraction and the first moment of the helicity distribution. The simulations have been performed using two $N_f{=}2$ and $N_f{=}2{+}1{+}1$ ensembles. Both ensembles have a twisted mass action with a clover term with the quark masses fixed at their physical values (physical point) and volumes of $64^3{\times}128$. The extracted quantities are compared with results from an existing $N_f{=}2$ ($48^3{\times}96$) ensemble. This comparison allows one to address volume and quenching effects.

hep-lat↗

arXiv2019

O(3) nonlinear sigma model in 1+1 dimensions with matrix product states

We numerically study the spectral properties, the entanglement and the zero-temperature phase structure at nonvanishing chemical potential of the O(3) nonlinear sigma model. Using matrix product states, a particular kind of one-dimensional tensor network state, we show that we are able to reach the asymptotic scaling regime and to reproduce the analytical predictions for the mass gap at vanishing chemical potential. In addition, we study the scaling of the entanglement entropy towards the continuum limit obtaining a central charge consistent with 2. Moreover, our approach does not suffer from the sign problem and we also explore the phase structure of the model for nonzero chemical potential and map out the location of the transitions between different charge sectors with high precision.

hep-lat↗

arXiv2019

Integrating Gauge Fields in the $ζ$-formulation of Feynman's path integral

In recent work by the authors, a connection between Feynman's path integral and Fourier integral operator $ζ$-functions has been established as a means of regularizing the vacuum expectation values in quantum field theories. However, most explicit examples using this regularization technique to date, do not consider gauge fields in detail. Here, we address this gap by looking at some well-known physical examples of quantum fields from the Fourier integral operator $ζ$-function point of view.

math-ph↗

arXiv2019

Systematic uncertainties in parton distribution functions from lattice QCD simulations at the physical point

We present a detailed study of the helicity-dependent and helicity-independent collinear parton distribution functions (PDFs) of the nucleon, using the quasi-PDF approach. The lattice QCD computation is performed employing twisted mass fermions with a physical value of the light quark mass. We give a systematic and in-depth account of the salient features entering in the evaluation of quasi-PDFs and their relation to the light-cone PDFs. In particular, we give details for the computation of the matrix elements, including the study of the various sources of systematic uncertainties, such as excited states contamination. In addition, we discuss the non-perturbative renormalization scheme used here and its systematics, effects of truncating the Fourier transform and different matching prescriptions.

hep-lat↗

arXiv2019

Finite-size scaling for four-dimensional Higgs-Yukawa model near the Gaussian fixed point

We analyse finite-size scaling behaviour of a four-dimensional Higgs-Yukawa model near the Gaussian infrared fixed point. Through improving the mean-field scaling laws by solving one-loop renormalisation group equations, the triviality property of this model can be manifested in the volume-dependence of moments of the scalar-field zero mode. The scaling formulae for the moments are derived in this work with the inclusion of the leading-logarithmic corrections. To test these formulae, we confront them with data from lattice simulations in a simpler model, namely the O(4) pure scalar theory, and find numerical evidence of good agreement. Our results of the finite-size scaling can in principle be employed to establish triviality of Higgs-Yukawa models, or to search for alternative scenarios in studying their fixed-point structure, if sufficiently large lattices can be reached.

hep-lat↗

arXiv2018

Tensor Networks and their use for Lattice Gauge Theories

Tensor Network States are ansätze for the efficient description of quantum many-body systems. Their success for one dimensional problems, together with the fact that they do not suffer from the sign problem and can address the simulation of real time evolution, have turned them into one of the most promising techniques to study strongly correlated systems. In the realm of Lattice Gauge Theories they can offer an alternative to standard lattice Monte Carlo calculations, which are suited for static properties and regimes where no sign problem appears. The application of Tensor Networks to this kind of problems is a young but rapidly evolving research field. This paper reviews some of the recent progress in this area, and how, using one dimensional models as testbench, some fundamental milestones have been reached that may pave the way to more ambitious goals.

hep-lat↗

arXiv2018

Light-cone PDFs from Lattice QCD

Using the approach proposed a few years ago by X. Ji, it has become feasible to extract parton distribution functions (PDFs) from lattice QCD, a task thought to be extremely difficult before Ji's proposal. In this talk, we discuss this approach, in particular different systematic effects that need to be controlled to ultimately have precise determinations of PDFs. Special attention is paid to the analysis of excited states. We emphasize that it is crucial to control excited states contamination and we show an analysis thereof for our lattice data, used to calculate quasi-PDFs and finally light-cone PDFs in the second part of this proceeding (C. Alexandrou et al., Quasi-PDFs from Twisted mass fermions at the physical point).

hep-lat↗

arXiv2018

Quasi-PDFs from Twisted mass fermions at the physical point

We present results for the flavor non-singlet u-d parton distribution functions within the nucleon using the quasi-PDF approach. The lattice calculation is performed by employing the twisted mass formulation and two gauge ensembles, having $N_f = 2$ and $N_f = 2 + 1 + 1$ dynamical fermions with masses tuned to their physical value. For the $N_f = 2$ physical point ensemble, the unpolarized, helicity and transversity distributions are computed for three values of the nucleon momentum, namely [6, 8, 10]$π/L$ corresponding to [0.83,1.11,1.38] GeV. Upon renormalization, we find that, as the nucleon momentum increases, the lattice results approach the phenomenological distributions resulting from analyses of deep inelastic scattering data, opening a promising path for a direct evaluation of parton distributions from the QCD Lagrangian. For the $N_f = 2 + 1 + 1$ physical point ensemble, we present preliminary results for the unpolarized distribution extracted from a nucleon boosted by $8π/L$ or 0.97 GeV.

hep-lat↗

arXiv2018

Nucleon spin structure from lattice QCD

In this lattice QCD study we evaluate the nucleon spin decomposition to quarks and gluons contributions. We employ one gauge ensemble of maximally twisted mass fermions with two degenerate light quarks tuned to approximately reproduce the physical pion mass. We find that both spin sum and momentum sum are satisfied within the current statistical and systematic accuracy.

hep-lat↗

arXiv2018

Connected and disconnected contributions to nucleon axial form factors using $N_f=2$ twisted mass fermions at the physical point

We present results on the isovector and isoscalar nucleon axial form factors including disconnected contributions,using an ensemble of $N_f =2$ twisted mass clover- improved Wilson fermions simulated with approximately the physical value of the pion mass. The light disconnected quark loops are computed using exact deflation, while the strange and the charm quark loops are evaluated using the truncated solver method. Techniques such as the summation and the two-state fits have been employed to access ground-state dominance.

hep-lat↗