An exact Polynomial Hybrid Monte Carlo algorithm for dynamical Kogut-Susskind fermions

We describe a Fourier Accelerated Hybrid Monte Carlo algorithm suitable for dynamical fermion simulations of non-gauge models. We test the algorithm in supersymmetric quantum mechanics viewed as a one-dimensional Euclidean lattice field theory. We find dramatic reductions in the autocorrelation time of the algorithm in comparison to standard HMC.

Smeared link fermionic actions can be straightforwardly simulated with partial-global updating. The efficiency of this simulation is greatly increased if the fermionic matrix is written as a product of several near-identical terms. Such a break-up can be achieved using polynomial approximations for the fermionic matrix. In this paper we will focus on methods of determining the optimum polynomials.

This is the write-up of three lectures on algorithms for dynamical fermions that were given at the ILFTN workshop 'Perspectives in Lattice QCD' in Nara during November 2005. The first lecture is on the fundamentals of Markov Chain Monte Carlo methods and introduces the Hybrid Monte Carlo (HMC) algorithm and symplectic integrators; the second lecture covers topics in approximation theory and thereby introduces the Rational Hybrid Monte Carlo (RHMC) algorithm and ways of evadin...

In this work we present a novel quantum Monte-Carlo method for fermions, based on an exact decomposition of the Boltzmann operator $exp(-\beta H)$. It can be seen as a synthesis of several related methods. It has the advantage that it is free of discretization errors, and applicable to general interactions, both for ground-state and finite-temperature calculations. The decomposition is based on low-rank matrices, which allows faster calculations. As an illustration, the metho...

In this work we present a detailed study of the Fermion Monte Carlo algorithm (FMC), a recently proposed stochastic method for calculating fermionic ground-state energies [M.H. Kalos and F. Pederiva, Phys. Rev. Lett. vol. 85, 3547 (2000)]. A proof that the FMC method is an exact method is given. In this work the stability of the method is related to the difference between the lowest (bosonic-type) eigenvalue of the FMC diffusion operator and the exact fermi energy. It is show...

We propose a Monte Carlo algorithm to promote Kennedy and Kuti's linear accept/reject algorithm which accommodates unbiased stochastic estimates of the probability to an exact one. This is achieved by adopting the Metropolis accept/reject steps for both the dynamical and noise configurations. We test it on the five state model and obtain desirable results even for the case with large noise. We also discuss its application to lattice QCD with stochastically estimated fermion d...

We describe a new Hybrid Monte Carlo (HMC) algorithm for dynamical overlap fermions, which improves the rate of topological index changes by adding an additional (intensive) term to the action for the molecular dynamics part of the algorithm. The metropolis step still uses the exact action, so that the Monte Carlo algorithm still generates the correct ensemble. By tuning this new term, we hope to be able to balance the acceptance rate of the HMC algorithm and the rate of topo...

The increase with time of computer resources devoted to simulations of full QCD is spectacular. Yet the reduction of systematic errors is comparatively slow. This is due to the algorithmic complexity of the problem. I review, in elementary terms, the origin of this complexity, and estimate it for 3 exact fermion algorithms.

Monte Carlo is a versatile and frequently used tool in statistical physics and beyond. Correspondingly, the number of algorithms and variants reported in the literature is vast, and an overview is not easy to achieve. In this pedagogical review, we start by presenting the probabilistic concepts which are at the basis of the Monte Carlo method. From these concepts the relevant free parameters--which still may be adjusted--are identified. Having identified these parameters, mos...

We investigate the critical dynamics of the Hybrid Monte Carlo algorithm approaching the chiral limit of standard Wilson fermions. Our observations are based on time series of lengths O(5000) for a variety of observables. The lattice sizes are 16^3 x 32 and 24^3 x 40. We work at beta=5.6, and kappa=0.156, 0.157, 0.1575, 0.158, with 0.83 > m_pi/m_rho > 0.55. We find surprisingly small integrated autocorrelation times for local and extended observables. The dynamical critical e...