Report on the CECAM/ESF STRUC-Fk Workshop on the Diffusion Quantum Monte Carlo Method
Summary of Workshop
A total of 34 participants from 9 countries attended the workshop held at CECAM from 19 to 21 September 2002. 19 talks and one discussion session covered a wide range of topics from new technical developments to applications of the Diffusion Quantum Monte Carlo (DMC) Method.
The format of the conference gave ample time for discussion, which proved to be extremely useful and productive. The different backgrounds of the participants (mainly physicists and chemists) allowed substantial and fruitful cross-fertilisation. The lively discussions also revealed the high level of activity in the field, which this workshop also served to steer and stimulate.
Brief description of the talks
The first day of the workshop was mainly taken up with talks on variants of the DMC method and on the fixed-node constraint. Michel Caffarel described the possible benefits and drawbacks of the "Pure DMC" method. Cyrus Umrigar described possible algorithms which do not use the fixed-node approximation and possible improvements to the accuracy and efficiency of fixed node algorithms. Mal Kalos described an extension of the DMC algorithm which solves the fermion sign problem, and showed that the new algorithm is stable when dealing with a system of 54 3He atoms in periodic boundary conditions. Dario Bressanini discussed the form of the nodal surfaces of simple systems, with the goal of developing a way to parameterise the nodes and optimize them directly. Roland Assaraf described new ideas about how to compute observables other than the energy to high accuracy. Heinz-Jiirgen Flad proposed a Jastrow factor expressed in a wavelet basis which could be used in DMC calculations and other many-particle methods. The final two talks of the day focussed on applications of the DMC method. Saverio Moroni talked about calculations on 4He droplets aimed at probing superfluid behaviour in confined systems. David Benoit discussed applications to vibrational states of molecules, gaining insight into hydrogen bonding.
The second day of the workshop was concerned with applications of the DMC method, with an emphasis on large systems. Andrew Williamson described highly efficient techniques for dealing with large systems in which the wave functions can be represented by strongly localised orbitals, and presented applications of these methods to semiconductor nanostructures. Ivan Stich presented results for atomic clusters, while Pietro Ballone's talk dealt with the homogeneous jellium system and with jellium clusters. Matthew Foulkes discussed the problem of calculating the surface energy of jellium, including finite size effects and the small energy differences which must be resolved. Dario Alfe described calculations on the diamond => Beta-tin phase transition in silicon. The results were not in close agreement with experiment, and a number of possible sources of error were investigated. The day ended with a discussion led by Cyrus Umrigar on the accuracy of DMC calculations. A number of participants presented thoughts and results on time-step errors, pseudopotential errors and finite-size errors. This discussion was very fruitful, exposing problems with present calculations and avenues for further investigation.
The final day of the workshop started with a presentation by Erik Koch of results on lattice models of doped fullerenes. Very interestingly, DMC calculations of the spectral function showed excellent agreement with exact diagonalisation studies. John Trail described mean-field and DMC studies of Wigner crystals. The next three talks concerned the optimisation of trial wave functions. Stephen Fahy described a numerical method for minimising the energy with respect to parameters in the wave function. Peter Nightingale described an elegant generalisation of the standard variance minimisation optimisation procedure which can be applied to excited states. Friedemann Schautz described a method for optimising configuration-interaction coefficients in trial wave functions based on similar ideas to those described in Stephen Fahy's talk. Lubos Mitas presented results for various nanoclusters. In the last talk of the workshop Arne Lizchow presented results for distributed multipole moments and polarisabilities including an analysis of the nodal errors. He also described some ideas on efficient calculations related to those presented earlier in the workshop by Andrew Williamson.
Conclusions
This workshop proved to be a great success. The presentations covered both methodological developments and applications of DMC methods. Stimulating and useful discussions covered most of the areas of interest to the community using these methods.
The popularity of the workshop and the growing number of international groups working in this area suggest that another workshop should be held on this topic within the next few years.
Organisers
Richard Needs, Cavendish Laboratory, University of Cambridge, UK
Claudia Filippi, Universiteit Leiden Instituut-Lorentz for Theoretical Physics, The Netherlands
Mike Towler, Cavendish Laboratory, University of Cambridge, UK
More details may be found in newsletter 54 from page 64