Rational Hybrid Monte Carlo Algorithm Research Articles

Controlling excited-state contamination in nucleon matrix elements

We present a detailed analysis of methods to reduce statistical errors and excited-state contamination in the calculation of matrix elements of quark bilinear operators in nucleon states. All the calculations were done on a 2+1 flavor ensemble with lattices of size $32^3 \times 64$ generated using the rational hybrid Monte Carlo algorithm at $a=0.081$~fm and with $M_\pi=312$ MeV. The statistical precision of the data is improved using the all-mode-averaging method. We compare two methods for reducing excited-state contamination: a variational analysis and a two-state fit to data at multiple values of the source-sink separation $t_{\rm sep}$. We show that both methods can be tuned to significantly reduce excited-state contamination and discuss their relative advantages and cost-effectiveness. A detailed analysis of the size of source smearing used in the calculation of quark propagators and the range of values of $t_{\rm sep}$ needed to demonstrate convergence of the isovector charges of the nucleon to the $t_{\rm sep} \to \infty $ estimates is presented.

Parallel software for lattice [formula omitted] supersymmetric Yang–Mills theory

We present new parallel software, SUSY LATTICE, for lattice studies of four-dimensional N=4 supersymmetric Yang–Mills theory with gauge group SU(N). The lattice action is constructed to exactly preserve a single supersymmetry charge at non-zero lattice spacing, up to additional potential terms included to stabilize numerical simulations. The software evolved from the MILC code for lattice QCD, and retains a similar large-scale framework despite the different target theory. Many routines are adapted from an existing serial code (Catterall and Joseph, 2012), which SUSY LATTICE supersedes. This paper provides an overview of the new parallel software, summarizing the lattice system, describing the applications that are currently provided and explaining their basic workflow for non-experts in lattice gauge theory. We discuss the parallel performance of the code, and highlight some notable aspects of the documentation for those interested in contributing to its future development. Program summaryProgram title: SUSY LATTICECatalogue identifier: AELS_v2_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AELS_v2_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 72821No. of bytes in distributed program, including test data, etc.: 1294754Distribution format: tar.gzProgramming language: C.Operating system: Any, tested on Linux workstations and MPI clusters with InfiniBand.Has the code been vectorized or parallelized?: Code is parallelizedClassification: 11.5.Catalogue identifier of previous version: AELS_v1_0Journal reference of previous version: Comput. Phys. Comm. 183 (2012) 1336.External routines: Lapack, Blas, Primme (optional)Does the new version supersede the previous version?: YesNature of problem: To carry out non-perturbative Monte Carlo importance sampling for maximally supersymmetric Yang–Mills theories in two and four dimensions, and thereby compute observables including Wilson loops, fermion bilinears, eigenvalues of D†D and the Pfaffian of the sparse fermion operator D.Solution method: The central application is a rational hybrid Monte Carlo algorithm with a two-level Omelyan molecular dynamics integrator. Gauge field configurations generated by this application may be saved to disk for subsequent measurements of additional observables. Input parameters for either configuration generation or analysis may be entered manually or read from a file.Reasons for new version: The code is parallelized to improve performance and scalability. In addition, several new features and measurements are provided.Summary of revisions: The program is completely rewritten on the basis of the MILC code for lattice QCD, and several new features and measurements are added.Restrictions: The code is currently restricted to two-dimensional N=(2,2) and four-dimensional N=4 supersymmetric Yang–Mills theories. The process of topological twisting on which it is based can also be applied to a few other systems, as discussed in Sections 1 and 5.Additional comments: Further documentation is provided in the distribution file, including a set of test runs with reference output in the testsuite directory.Running time: From seconds to hours depending on the computational task, lattice volume, gauge group, and desired statistics, as well as on the computing platform and number of cores used. For example, rational hybrid Monte Carlo generation of 50 molecular dynamics time units for a 163×32 lattice volume with gauge group U(2) takes approximately 16 hours on 512 cores of the USQCD bc cluster at Fermilab, while standard measurements on a saved 83×24 U(2) configuration require only 8 seconds on one eight-core workstation.

Exact pseudofermion action for Monte Carlo simulation of domain-wall fermion

We present an exact pseudofermion action for hybrid Monte Carlo simulation (HMC) of one-flavor domain-wall fermion (DWF), with the effective 4-dimensional Dirac operator equal to the optimal rational approximation of the overlap-Dirac operator with kernel H=cHw(1+dγ5Hw)−1, where c and d are constants. Using this exact pseudofermion action, we perform HMC of one-flavor QCD, and compare its characteristics with the widely used rational hybrid Monte Carlo algorithm (RHMC). Moreover, to demonstrate the practicality of the exact one-flavor algorithm (EOFA), we perform the first dynamical simulation of the (1+1)-flavors QCD with DWF.

An object oriented code for simulating supersymmetric Yang–Mills theories

We present SUSY_LATTICE – a C++ program that can be used to simulate certain classes of supersymmetric Yang–Mills (SYM) theories, including the well known N=4 SYM in four dimensions, on a flat Euclidean space–time lattice. Discretization of SYM theories is an old problem in lattice field theory. It has resisted solution until recently when new ideas drawn from orbifold constructions and topological field theories have been brought to bear on the question. The result has been the creation of a new class of lattice gauge theories in which the lattice action is invariant under one or more supersymmetries. The resultant theories are local, free of doublers and also possess exact gauge-invariance. In principle they form the basis for a truly non-perturbative definition of the continuum SYM theories. In the continuum limit they reproduce versions of the SYM theories formulated in terms of twisted fields, which on a flat space–time is just a change of the field variables. In this paper, we briefly review these ideas and then go on to provide the details of the C++ code. We sketch the design of the code, with particular emphasis being placed on SYM theories with N=(2,2) in two dimensions and N=4 in three and four dimensions, making one-to-one comparisons between the essential components of the SYM theories and their corresponding counterparts appearing in the simulation code. The code may be used to compute several quantities associated with the SYM theories such as the Polyakov loop, mean energy, and the width of the scalar eigenvalue distributions. Program summaryProgram title: SUSY_LATTICECatalogue identifier: AELS_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AELS_v1_0.htmlProgram obtainable from: CPC Program Library, Queenʼs University, Belfast, N. IrelandLicensing provisions: Standard CPC license, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 9315No. of bytes in distributed program, including test data, etc.: 95 371Distribution format: tar.gzProgramming language: C++Computer: PCs and WorkstationsOperating system: Any, tested on Linux machinesClassification:: 11.6Nature of problem: To compute some of the observables of supersymmetric Yang–Mills theories such as supersymmetric action, Polyakov/Wilson loops, scalar eigenvalues and Pfaffian phases.Solution method: We use the Rational Hybrid Monte Carlo algorithm followed by a Leapfrog evolution and a Metropolis test. The input parameters of the model are read in from a parameter file.Restrictions: This code applies only to supersymmetric gauge theories with extended supersymmetry, which undergo the process of maximal twisting. (See Section 2 of the manuscript for details.)Running time: From a few minutes to several hours depending on the amount of statistics needed.

2+1flavor domain wall QCD on a(2 fm)3lattice: Light meson spectroscopy withLs=16

We present results for light meson masses and pseudoscalar decay constants from the first of a series of lattice calculations with 2+1 dynamical flavors of domain wall fermions and the Iwasaki gauge action. The work reported here was done at a fixed lattice spacing of about 0.12 fm on a 16^3\times32 lattice, which amounts to a spatial volume of (2 fm)^3 in physical units. The number of sites in the fifth dimension is 16, which gives m_{res} = 0.00308(4) in these simulations. Three values of input light sea quark masses, m_l^{sea} \approx 0.85 m_s, 0.59 m_s and 0.33 m_s were used to allow for extrapolations to the physical light quark limit, whilst the heavier sea quark mass was fixed to approximately the physical strange quark mass m_s. The exact rational hybrid Monte Carlo algorithm was used to evaluate the fractional powers of the fermion determinants in the ensemble generation. We have found that f_\pi = 127(4) MeV, f_K = 157(5) MeV and f_K/f_\pi = 1.24(2), where the errors are statistical only, which are in good agreement with the experimental values.

Accelerating Dynamical-Fermion Computations Using the Rational Hybrid Monte Carlo Algorithm with Multiple Pseudofermion Fields

There has been much recent progress in the understanding and reduction of the computational cost of the hybrid Monte Carlo algorithm for lattice QCD as the quark mass parameter is reduced. In this letter we present a new solution to this problem, where we represent the fermionic determinant using n pseudofermion fields, each with an nth root kernel. We implement this within the framework of the rational hybrid Monte Carlo algorithm. We compare this algorithm with other recent methods in this area and find it is competitive with them.

Accelerating staggered-fermion dynamics with the rational hybrid Monte Carlo algorithm

Improved staggered-fermion formulations are a popular choice for lattice QCD calculations. Historically, the algorithm used for such calculations has been the inexact $R$ algorithm, which has systematic errors that only vanish as the square of the integration step size. We describe how the exact rational hybrid Monte Carlo (RHMC) algorithm may be used in this context, and show that for parameters corresponding to current state-of-the-art computations it leads to a factor of approximately seven decrease in cost as well as having no step-size errors.

Rational hybrid Monte Carlo algorithm for theories with unknown spectral bounds

The Rational Hybrid Monte Carlo (RHMC) algorithm extends the Hybrid Monte Carlo algorithm for lattice QCD simulations to situations involving fractional powers of the determinant of the quadratic Dirac operator. This avoids the updating increment (dt) dependence of observables which plagues the Hybrid Molecular-dynamics (HMD) method. The RHMC algorithm uses rational approximations to fractional powers of the quadratic Dirac operator. Such approximations are only available when positive upper and lower bounds to the operator's spectrum are known. We apply the RHMC algorithm to simulations of 2 theories for which a positive lower spectral bound is unknown: lattice QCD with staggered quarks at finite isospin chemical potential and lattice QCD with massless staggered quarks and chiral 4-fermion interactions ({chi}QCD). A choice of lower bound is made in each case, and the properties of the RHMC simulations these define are studied. Justification of our choices of lower bounds is made by comparing measurements with those from HMD simulations, and by comparing different choices of lower bounds.

Perturbative Wilson loops from unquenched Monte Carlo simulations at weak couplings

Perturbative expansions of several small Wilson loops are computed through next-to-next-to-leading order in unquenched lattice QCD, from Monte Carlo simulations at weak couplings. This approach provides a much simpler alternative to conventional diagrammatic perturbation theory, and is applied here for the first time to full QCD. Two different sets of lattice actions are considered: one set uses the unimproved plaquette gluon action together with the unimproved staggered-quark action; the other set uses the one-loop-improved Symanzik gauge-field action together with the so-called ``asqtad'' improved-staggered quark action. Simulations are also done with different numbers of dynamical fermions. An extensive study of the systematic uncertainties is presented, which demonstrates that the small third-order perturbative component of the observables can be reliably extracted from simulation data. We also investigate the use of the rational hybrid Monte Carlo algorithm for unquenched simulations with unimproved-staggered fermions. Our results are in excellent agreement with diagrammatic perturbation theory, and provide an important cross-check of the perturbation theory input to a recent determination of the strong coupling $\alpha_{\bar{\rm MS}}(M_Z)$ by the HPQCD collaboration.

The RHMC algorithm for 2 flavours of dynamical staggered fermions

We describe an implementation of the Rational Hybrid Monte Carlo (RHMC) algorithm for dynamical computations with two flavours of staggered quarks. We discuss several variants of the method, the performance and possible sources of error for each of them, and we compare the performance and results to the inexact R algorithm.

A new exact method for dynamical fermion computations with non-local actions

We introduce a new algorithm which we call the Rational Hybrid Monte Carlo Algorithm (RHMC). This method uses a rational approximation to the fermionic kernel together with a noisy (Kennedy-Kuti [1]) acceptance step to give an efficient algorithm with no molecular dynamics integration step-size errors.