Department of Physics and Mathematical Physics, **Machine** VP

University of Adelaide

**Co-Investigators** Lindsay R Dodd and Armin Ardekani

Department of Physics and Mathematical Physics, University of Adelaide

**Research in Computational Physics**

The central aim of this work is to use modern supercomputers to extend our understanding of some of the more complex behaviour exhibited by fundamental theories of matter. This project is concerned with the investigation of the nonperturbative behaviour of quantum field theories with some emphasis on understanding the quark substructure of the atomic nucleus and the associated strong forces which bind the nucleus together. The investigative techniques involve the simulation of field theories on a discrete space-time lattice. We propose to study phase transitions in various model field theories and to study the formation of bound states and extended structures in these theories.

**What are the basic questions addressed?**

As an initial step we are studying the pure boson sector of theories (i.e., without fermions) such as in 2-dimensions. A motivating aspect of this work is the ability to study extended objects (called `kinks') on the lattice, which can then be directly compared to semiclassical configurations. In addition these simple models can be used to develop our understanding of spontaneous symmetry breaking, which we know takes place in both quantum chromodynamics (QCD) (the elementary theory of the strong interactions) and in the so-called standard model (the theory which unifies the weak and electromagnetic interactions). Also underway is the extension of these techniques to include fermions, to work in higher dimensions, and to directly study QCD itself. The latter work on QCD is highly computer intensive and is being carried out in collaboration with K F Liu and his group at the University of Kentucky in the USA.

**What are the results to date and the future of the work?**

We have obtained some configurations for models including dynamical fermions and some expected difficulties have become apparent. The generation of configurations is very time-consuming so that direct study of the critical limits which is necessary to obtain physical results may not be the optimal approach. We are therefore examining the possibility of using a combination of analytical and numerical methods to extract information from the simulations. Renormalization group techniques can be applied in certain circumstances. The program has been checked for the Gaussian Model (i.e., for the free field theory of a system of non-interacting bosons). The correlation functions (propagators) on the lattice were measured and agree with the analytic forms which are known. Extraction of the particle mass from the correlation length on the lattice was found to have significant systematic finite size effects. An alternative pole definition of the mass was found to be more accurate. Last year we began work on a simplified Yukawa model in which we treat the dynamical fermions as a background field. But in the search for a method to extract parameters of the model from lattice calculations as precisely as possible, we found that the effective potential method was statistically superior. We are systematically investigating this method by applying it to scalar field theory with a quartic interaction in two dimensions and comparing our results with 2-loop calculations. We then want to also examine this method in the strong coupling regime.

We will not pursue the lattice guage component of this project in collaboration with Professor Keh-Fei Liu at the University of Kentucky until additional local personnel join the project. The vector programs so far written are very efficient and the percentage of vectorization is around 90%. In the current stage of our work we anticipate making much more extensive use of the machine and its memory.

**What computational techniques are used and why is a supercomputer
required?**

The basic ingredients of lattice based studies are degrees of freedom on a lattice representing space-time and Monte-Carlo methods to simulate the dynamics of the physical system. The specific algorithm used here is the Hybrid Monte Carlo method, which combines the best features of the deterministic integration of the equations of motion (leap frog algorithm) and importance sampling (Metropolis method). As the limit of large lattices is taken the computational power needed grows extremely rapidly, meaning that forefront calculations necessarily require the fastest available supercomputers.