Critical slowing down and error analysis in lattice QCD simulations

Abstract

We study the critical slowing down towards the continuum limit of lattice QCD simulations with Hybrid Monte Carlo type algorithms. In particular for the squared topological charge we find it to be very severe with an effective dynamical critical exponent of about 5 in pure gauge theory. We also consider Wilson loops which we can demonstrate to decouple from the modes which slow down the topological charge. Quenched observables are studied and a comparison to simulations of full QCD is made. In order to deal with the slow modes in the simulation, we propose a method to incorporate the information from slow observables into the error analysis of physical observables and arrive at safer error estimates.

33 pages including 15 figures and 4 tables

References in corpus (36)

• A New Way to Set the Energy Scale in Lattice Gauge Theories and its Application to the Static Force and ${\alpha }_s$ in SU(2) Yang--Mills Theory
• Properties and uses of the Wilson flow in lattice QCD
• Flavor Symmetry and the Static Potential with Hypercubic Blocking
• Analytic Smearing of SU(3) Link Variables in Lattice QCD
• Chiral symmetry and O(a) improvement in lattice QCD
• Non-perturbative O(a) improvement of lattice QCD
• Perturbative analysis of the gradient flow in non-abelian gauge theories
• The Nf=0 heavy quark potential from short to intermediate distances
• Trivializing maps, the Wilson flow and the HMC algorithm
• Monte Carlo errors with less errors
• Speeding up the Hybrid-Monte-Carlo algorithm for dynamical fermions
• Accelerating Dynamical Fermion Computations using the Rational Hybrid Monte Carlo (RHMC) Algorithm with Multiple Pseudofermion Fields
• O(a) improvement of lattice QCD with two flavors of Wilson quarks
• Schwarz-preconditioned HMC algorithm for two-flavour lattice QCD
• Theta dependence of SU(N) gauge theories
• Critical Exponents of the 3D Ising Universality Class From Finite Size Scaling With Standard and Improved Actions
• Enhanced chiral logarithms in partially quenched QCD
• Quark mass dependence of hadron masses from lattice QCD
• Critical slowing down of topological modes
• Hybrid Monte Carlo and topological modes of full QCD
• A Monte Carlo study of leading order scaling corrections of phi^4 theory on a three dimensional lattice
• Universality of the topological susceptibility in the SU(3) gauge theory
• Maximal variance reduction for stochastic propagators with applications to the static quark spectrum
• The Making of the Standard Model
• Non-perturbative improvement of the axial current for dynamical Wilson fermions
• Cost of the Generalised Hybrid Monte Carlo Algorithm for Free Field Theory
• Exploring the HMC trajectory-length dependence of autocorrelation times in lattice QCD
• Topological susceptibility with the improved Asqtad action
• Light hadron spectroscopy in two-flavor QCD with small sea quark masses
• Topology, the Wilson flow and the HMC algorithm
• Quark mass effects on the topological susceptibility in QCD
• The Monte Carlo method in quantum field theory
• Leptonic Decays of $B$- and $D$-Mesons
• Lattice cutoff effects for F_Ds with improved Wilson fermions - a final lesson from the quenched case
• Topological susceptibility with the improved Asqtad action
• Preparing for N_f=2 simulations at small lattice spacings

Cited by in corpus (176)

• FLAG Review 2019
• Review of lattice results concerning low energy particle physics
• Domain wall QCD with physical quark masses
• Simulation of QCD with N_f=2+1 flavors of non-perturbatively improved Wilson fermions
• Machine Learning in Nuclear Physics
• Large-Momentum Effective Theory
• Lattice QCD with open boundary conditions and twisted-mass reweighting
• The strange quark mass and Lambda parameter of two flavor QCD
• Lattice QCD without topology barriers
• A Trailhead for Quantum Simulation of SU(3) Yang-Mills Lattice Gauge Theory in the Local Multiplet Basis
• Quantum Computing for High-Energy Physics: State of the Art and Challenges. Summary of the QC4HEP Working Group
• Setting the scale for the CLS $2+1$ flavor ensembles
• Light Hadron Masses from Lattice QCD
• Axion phenomenology and $\theta$-dependence from $N_f=2+1$ lattice QCD
• Finite temperature study of the axial U(1) symmetry on the lattice with overlap fermion formulation
• The strong coupling from a nonperturbative determination of the $\Lambda$ parameter in three-flavor QCD
• $I=1$ and $I=2$ $\pi -\pi$ scattering phase shifts from $N_{\mathrm{f}}=2+1$ lattice QCD
• Charmed baryon spectroscopy and light flavour symmetry from lattice QCD
• Simulating twisted mass fermions at physical light, strange and charm quark masses
• The $I=1$ pion-pion scattering amplitude and timelike pion form factor from $N_{\mathrm{f}}=2+1$ lattice QCD
• Confirming the Existence of the strong CP Problem in Lattice QCD with the Gradient Flow
• Improvement of N_f=3 lattice QCD with Wilson fermions and tree-level improved gauge action
• Phase Transitions in Particle Physics -- Results and Perspectives from Lattice Quantum Chromo-Dynamics
• Exploring QCD matter in extreme conditions with Machine Learning
• FLAG Review 2024
• The Low Energy Constants of $SU(2)$ Partially Quenched Chiral Perturbation Theory from $N_f=2+1$ Domain Wall QCD
• Hadro-quarkonium from Lattice QCD
• Topology in full QCD at high temperature: a multicanonical approach
• Nucleon electromagnetic form factors in two-flavour QCD
• Machine learning action parameters in lattice quantum chromodynamics
• Lattice QCD for Cosmology
• Lattice QCD and the anomalous magnetic moment of the muon
• Automatic differentiation for error analysis of Monte Carlo data
• Slow running of the Gradient Flow coupling from 200 MeV to 4 GeV in $N_{\mathrm{f}}=3$ QCD
• Topological susceptibility and the sampling of field space in $N_f=2$ lattice QCD simulations
• Determination of the Static Potential with Dynamical Fermions
• Lattice constraints on the thermal photon rate
• Determination of the QCD $\Lambda$-parameter and the accuracy of perturbation theory at high energies
• Isovector electromagnetic form factors of the nucleon from lattice QCD and the proton radius puzzle
• Efficient Modelling of Trivializing Maps for Lattice ${\varphi }^4$ Theory Using Normalizing Flows: A First Look at Scalability
• Flow-based sampling for fermionic lattice field theories
• The topological susceptibility in the large-N limit of SU(N) Yang-Mills theory
• Non-perturbative improvement of the axial current in N_f=3 lattice QCD with Wilson fermions and tree-level improved gauge action
• Step scaling and the Yang-Mills gradient flow
• pyerrors: a python framework for error analysis of Monte Carlo data
• Precision lattice QCD computation of the $B^{\ast }B\pi$ coupling
• Decay constants of B-mesons from non-perturbative HQET with two light dynamical quarks
• Thermal quarkonium physics in the pseudoscalar channel
• Fighting topological freezing in the two-dimensional CP${}^{N-1}$ model
• ${\eta }^{\prime }$ meson mass from topological charge density correlator in QCD
• The pion vector form factor from lattice QCD and NNLO chiral perturbation theory
• Topological susceptibility of $N_f=2+1$ QCD from staggered fermions spectral projectors at high temperatures
• The nucleon electric dipole moment with the gradient flow: the $\theta$-term contribution
• Towards glueball masses of large-$N$ $\mathrm{SU}(N)$ pure-gauge theories without topological freezing
• Scale setting and the light baryon spectrum in $N_f=2+1$ QCD with Wilson fermions
• Topological critical slowing down: variations on a toy model
• Flow-based sampling in the lattice Schwinger model at criticality
• Multiscale Monte Carlo equilibration: Pure Yang-Mills theory
• Metadynamics Surfing on Topology Barriers: the $C{P}^{N-1}$ Case
• Spectral density of the Dirac operator in two-flavour QCD
• Hybrid static potentials in SU(3) lattice gauge theory at small quark-antiquark separations
• Octet baryon isovector charges from $N_f=2+1$ lattice QCD
• Lattice study of a magnetic contribution to heavy quark momentum diffusion
• The gradient flow running coupling with twisted boundary conditions
• Advances in machine-learning-based sampling motivated by lattice quantum chromodynamics
• Chiral dynamics in the low-temperature phase of QCD
• Probing the chiral regime of Nf=2 QCD with mixed actions
• Chiral symmetry breaking in QCD Lite
• Topological properties of $C{P}^{N-1}$ models in the large-$N$ limit
• Diffusion Models as Stochastic Quantization in Lattice Field Theory
• Topological sampling through windings
• Uncertainty Quantification in Lattice QCD Calculations for Nuclear Physics
• The b-quark mass from non-perturbative $N_f=2$ Heavy Quark Effective Theory at $O(1/m_h)$
• Comparison of the mass preconditioned HMC and the DD-HMC algorithm for two-flavour QCD
• Power corrections from decoupling of the charm quark
• Fractional instanton of the SU($3$) gauge theory in weak coupling regime
• Lattice determinations of the strong coupling
• The Large $N_c$ limit of QCD on the lattice
• How perturbative are heavy sea quarks?
• Diffusion of topological charge in lattice QCD simulations
• Effects of non-equilibrated topological charge distributions on pseudoscalar meson masses and decay constants
• Testing trivializing maps in the Hybrid Monte Carlo algorithm
• Electromagnetic form factors of the nucleon from $N_f=2+1$ lattice QCD
• Towards reduction of autocorrelation in HMC by machine learning
• The topological susceptibility of two-dimensional $U(N)$ gauge theories
• On fits to correlated and auto-correlated data
• An exploratory study of heavy domain wall fermions on the lattice
• Ergodic sampling of the topological charge using the density of states
• Past, present, and future of precision determinations of the QCD coupling from lattice QCD
• SU(3) Yang Mills theory at small distances and fine lattices
• Leading order mesonic and baryonic SU(3) low energy constants from $N_f=3$ lattice QCD
• Topological susceptibility of QCD with dynamical Möbius domain wall fermions
• Continuum limit of the leading order HQET form factor in $B_s\to K\ell \nu$ decays
• Lattice QCD on Non-Orientable Manifolds
• Non-renormalizability of the HMC algorithm
• Optimising creation operators for charmonium spectroscopy on the lattice
• Light quark masses in N_f = 2+1 lattice QCD with Wilson fermions
• Interpreting Numerical Measurements in Fixed Topological Sectors
• Muon $g-2$: Lattice calculations of the hadronic vacuum polarization
• The Yang-Mills gradient flow and renormalization
• An efficient finite-resource formulation of non-Abelian lattice gauge theories beyond one dimension
• Algorithms for lattice QCD: progress and challenges
• Topological aspects of G2 Yang-Mills theory
• Scaling properties of multiscale equilibration
• Wilson fermions at fine lattice spacings: scale setting, pion form factors and (g-2)_mu
• Recent progress on QCD inputs for axion phenomenology
• Determination of the charm quark mass in lattice QCD with $2+1$ flavours on fine lattices
• Non-perturbative determination of improvement coefficients b_m and b_A-b_P and normalisation factor Z_m*Z_P/Z_A with N_f=3 Wilson fermions
• How much do charm sea quarks affect the charmonium spectrum?
• Extraction of bare Form Factors for ${\mathrm{B}}_{\mathrm{s}}\to \mathrm{K}\ell \nu$ Decays in non-perturbative HQET
• The renormalised $\mathrm{O}(a)$ improved vector current in three-flavour lattice QCD with Wilson quarks
• The shape of the static potential with dynamical fermions
• A lattice calculation of the hadronic vacuum polarization contribution to $(g-2{)}_{\mu }$
• Machine learning a fixed point action for SU(3) gauge theory with a gauge equivariant convolutional neural network
• Multiscale Monte Carlo equilibration: Two-color QCD with two fermion flavors
• Testing algorithms for critical slowing down
• Status and challenges of simulations with dynamical fermions
• B-meson spectroscopy in HQET at order 1/m
• Ratio of flavour non-singlet and singlet scalar density renormalisation parameters in $N_{\mathrm{f}}=3$ QCD with Wilson quarks
• Topological susceptibility in 2+1-flavor QCD with chiral fermions
• Generative learning for the problem of critical slowing down in lattice Gross Neveu model
• Fermions as Global Correction: the QCD Case
• Scale setting for $N_f=3+1$ QCD
• Parallel Tempered Metadynamics: Overcoming potential barriers without surfing or tunneling
• Sampling U(1) gauge theory using a re-trainable conditional flow-based model
• On learning higher-order cumulants in diffusion models
• Quantum mean estimation for lattice field theory
• Exploring autocorrelations in two-flavour Wilson Lattice QCD using DD-HMC algorithm
• Constructing static quark-anti-quark creation operators from Laplacian eigenmodes
• Strong CP problem in the quantum rotor
• Scaling of Stochastic Normalizing Flows in $\mathrm{SU}(3)$ lattice gauge theory
• Heavy Wilson Quarks and O($a$) Improvement: Nonperturbative Results for $b_{\mathrm{g}}$
• Ultraviolet filtering of lattice configurations and applications to Monte Carlo dynamics
• Machine-learned RG-improved gauge actions and classically perfect gradient flows
• Open-Boundary Conditions in the Deconfined Phase
• Multilevel Monte Carlo for quantum mechanics on a lattice
• Topology changing update algorithms for SU(3) gauge theory
• Reduced critical slowing down for statistical physics simulations
• Spanning of Topological sectors, charge and susceptibility with naive Wilson fermions
• B-physics from non-perturbatively renormalized HQET in two-flavour lattice QCD
• Thermal evolution of dark matter and gravitational-wave production in the early universe from a symplectic glueball model
• Charm physics with Moebius Domain Wall Fermions
• Building imaginary-time thermal field theory with artificial neural networks
• Topological observables and $\theta$ dependence in high temperature QCD from lattice simulations
• Ergodicity of the LLR method for the Density of States
• Hybrid static potentials in SU(2) lattice gauge theory at short quark-antiquark separations
• Minimal Autocorrelation in Hybrid Monte Carlo simulations using Exact Fourier Acceleration
• S-wave flavor-singlet meson mixing in QCD with light and charm quarks
• Scaling flow-based approaches for topology sampling in $\mathrm{SU}(3)$ gauge theory
• Decoupling of charm beyond leading order
• Topological Susceptibility under Gradient Flow
• Toward extracting scattering phase shift from integrated correlation functions on quantum computers
• Autocorrelations in Hybrid Monte Carlo Simulations
• Modifying the molecular dynamics action to increase topological tunnelling rate for dynamical overlap fermions
• Flow-based Nonperturbative Simulation of First-order Phase Transitions
• Lattice QCD with 2+1 Flavors and Open Boundaries: First Results of the Baryon Spectrum
• Thermal Simulations, Open Boundary Conditions and Switches
• Scaling, topological tunneling and actions for weak coupling DWF calculations
• B-physics with $N_f=2$ Wilson fermions
• The determination of potential scales in 2+1 flavor QCD
• Exploiting the hopping parameter expansion in the hybrid Monte Carlo (HMC) simulation of lattice QCD with two degenerate flavours of Wilson fermions
• Efficient computations of continuous action densities of states for lattice models
• A comparison of updating algorithms for large N reduced models
• Classifying Topological Charge in SU(3) Yang-Mills Theory with Machine Learning
• Wilson chiral perturbation theory for dynamical twisted mass fermions vs lattice data - a case study
• B $\to$ $\pi$ form factor with 2 flavours of $O(a)$ improved Wilson quarks
• News from the Lattice: example of the pion distribution amplitude
• A Fluctuation Theory of Topological Susceptibility
• Efficient identification of critical regions via Flow Matching-based Monte Carlo initialization
• Generalized HMC using Nambu mechanics for lattice QCD
• Memory efficient finite volume schemes with twisted boundary conditions
• Hadronic decay of vector charmonium from the lattice
• Extracting the ${\eta }^{\prime }$ meson mass from gluonic correlators in lattice QCD
• Scale setting of SU($N$) Yang--Mills theory, topology and large-$N$ volume independence
• Tuning of the strange quark mass with optimal reweighting
• Non-perturbative Heavy Quark Effective Theory: An application to semi-leptonic B-decays