A.D. Kennedy

Hybrid Monte Carlo

We present a new method for the numerical simulation of lattice field theory. A hybrid (molecular dynamics/Langevin) algorithm is used to guide a Monte Carlo simulation. There are no discretization errors even for large step sizes. The method is especially efficient for systems such as quantum chromodynamics which contain fermionic degrees of freedom. Detailed results are presented for four-dimensional compact quantum electrodynamics including the dynamical effects of electrons.

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

Abstract 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.

Acceptances and autocorrelations in hybrid Monte Carlo

Abstract We present the results of an analytic study of the Hybrid Monte Carlo algorithm for free field theory. We calculate the acceptance rate and autocorrelation function as a function of lattice volume, integration step size, and (average) trajectory length. We show that the dynamical critical exponent z can be tuned to unity by a judicious choice of average trajectory length.

The QCD finite temperature transition and hybrid Monte Carlo

Using the hybrid Monte Carlo method we consider lattice quantum chromodynamics with Kogut-Susskind staggered fermions on 43 × 4, 63 × 4, 83 × 4 lattices with m = 0.1. Applying finite size scaling methods for a first-order phase transition we find some evidence for a two-phase state.

The heavy quark potential in QCD with 2 flavors of dynamical quarks

Abstract We compute the heavy quark potential on configurations generated by the HEMCGC Collaboration with dynamical staggered fermions at 6/g2=5.6 and with dynamical Wilson fermions at 6/g2= 5.3. The computations are done on 163 × 32 lattices, corresponding to physical sizes of about 1.6 and 2.3 fm, respectively. Up to the distances probed no sign of string breaking is detectable. We also compute the recently proposed scale r0 defined by r02F(r0) = 1.65.

Instabilities and non-reversibility of molecular dynamics trajectories

Abstract The theoretical justification of the Hybrid Monte Carlo algorithm depends upon the molecular dynamics trajectories within it being exactly reversible. If computations were carried out with exact arithmetic then it would be easy to ensure such reversibility, but the use of approximate floating point arithmetic inevitably introduces violations of reversibility. In the absence of evidence to the contrary, we are usually prepared to accept that such rounding errors can be made small enough to be innocuous, but in certain circumstances they are exponentially amplified and lead to blatantly erroneous results. We show that there are two types of instability of the molecular dynamics trajectories which lead to this behavior, instabilities due to insufficiently accurate numerical integration of Hamiltons equations, and intrinsic chaos in the underlying continuous fictitious time equations of motion themselves. We analyze the former for free field theory, and show that it is essentially a finite-volume effect. For the latter we propose a hypothesis as to how the Liapunov exponent describing the chaotic behavior of the fictitious time equations of motion for an asymptotically free quantum field theory behaves as the system is taken to its continuum limit, and explain why this means that instabilities in molecular dynamics trajectories are not a significant problem for Hybrid Monte Carlo computations. We present data for pure SU(3) gauge theory and for QCD with dynamical fermions on small lattices to illustrate and confirm some of our results.

Hybrid Monte Carlo and quantum chromodynamics

Abstract In this paper we study the properties of the hybrid Monte Carlo algorithm applied to lattice quantum chromodynamics including the dynamical effects of fermions. We find that this “exact” method performs very well on 44 lattices, and shows considerable promise for being a practicable means with which to undertake realistic Monte Carlo computations of fermionic systems.

Thermodynamics of lattice QCD with two light quarks on a 16(3) x 8 lattice.

We have extended our earlier simulations of the high temperature behaviour of lattice QCD with two light flavours of staggered quarks on a

A 0.5 teraflops machine optimized for lattice QCD

16^3 \times 8

The chiral limit and phase structure of QCD with Wilson fermions

lattice to lower quark mass (m_q=0.00625). The transition from hadronic matter to a quark-gluon plasma is observed at