Research

Seeing into the Quantum World

---by Randall Graham, Science Writer

``I work at the fundamental level trying to solve the original equations of quantum theory to build from the ground level an understanding of atomic structure,'' says UIUC Physics Professor and NCSA Research Scientist David Ceperley. ``A lot of the work I do is not really materials science, but the same mathematical problem.'' Ceperley's goal is to advance the field of materials science by developing computational techniques that can be applied broadly to many types of systems where quantum effects are important.

Over the years Ceperley has been working on methods to directly simulate the properties of hydrogen and helium. In one sense, these atoms are simple--having few electrons. In another sense, their behavior is especially complex since both their electrons and nuclei exhibit quantum motion--a property not found in heavier atoms.

``Hydrogen and helium are a little difficult to work with,'' says Ceperley, ``because the nuclei of these atoms are light; hence, they move around a lot. Most computational methods treat these nuclei simply as classical particles that do not have quantum motion.''

QMC techniques

Quantum Monte Carlo (QMC) methods--algorithms that use statistical sampling to solve the Schršdinger equation--are what Ceperley relies on. Quantum particles cannot have both their velocity and location measured at the same time, so scientists represent the particles as waves of probability--the probability that particles will be in a given location at any given time.

Ceperley sets simulated electrons into random motion based directly on the Schršdinger equation. In hydrogen and helium, both electrons and nuclei are set in motion. Next Ceperley takes many computational ``snapshots'' of his particles. By superimposing the results, a picture of average behavior begins to take shape.

QMC studies

Together with UIUC Physics Professor Richard Martin, Ceperley leads a 15-member group of postdoctoral research associates, visitors, and graduate students in theoretical condensed matter physics--a field which studies solids, liquids, and gases. QMC studies by the Ceperley-Martin group have revealed the behavior of helium atoms near the transition temperature where helium changes from an ordinary fluid to a superfluid. These calculations are of interest to Ceperley and Martin's colleagues in the UIUC Center for High-Temperature Superconductivity, of which they are associate members.

Similar computational methods allowed Ceperley and Berni Alder of Lawrence Livermore National Laboratory to calculate the arrangement of atoms in bulk hydrogen subjected to extremely high pressure and its transition from insulator to metal. Recently UIUC graduate student Vincent Natolie, Martin, and Ceperley predicted that hydrogen, at 3 Mbars (megabars), should form a crystal lattice similar to diamond.

These efforts require expanded computing power. For example, Werner Krauth, former NCSA postdoctoral research associate of Ceperley (now at the Ecole Normale Superior, Paris), pioneered the use of clustered workstations at NCSA. Krauth utilized the equivalent of 5,000 CPU hours of NCSA's CRAY Y-MP system on NCSA's networked SGI workstations for his research on the effect of disorder on superfluidity.

Clustered workstations are well-suited to QMC methods--many calculations can be conducted relatively independent of each other and then summed.

Exploring new architecture

``People are thinking about how to make their methods more efficient and do a chunk of a complex material like high- temperature superconductors,'' Ceperley says. ``The unit cell, or basic building block, may consist of a hundred atoms or more. Now they can think about putting the whole cell on the computer, whereas before they'd have to take only ten atoms.''

Ceperley is exploring the use of new architectures--specifically Thinking Machines' CM-5 system at NCSA--to perform calculations on the electronic structure of condensed matter in collaboration with UIUC Computer Science Professor Roy Campbell and Martin. Their project recently was awarded a grant from NSF's HPCC Computational Advances in Materials Research (CARM) Initiative [see access, October-December, 1992].

The group's goal is to develop methods using massively parallel processing (MPP) computers that can be applied to problems in experimental physics and materials science. They will study properties of materials such as silicon, condensed states of hydrogen, surfaces of metals, and liquid and amorphous systems, superlattices, and correlated electronic states in magnetic insulators.

These studies may lay the foundation for the development of the next generation of computational materials science. Possibly the power of MPP could be used to accurately describe and predict more complex materials and phenomena--such as correlations that lead to magnetism and superconductivity in transition metal compounds.

In another group effort, Ceperley is working with a multicenter collaboration on quantum simulations of molecules and materials. This project involves colleagues from Kent State, Cornell, Arizona State, and New York Universities; University of California at Berkeley; and Brooklyn College.

Ceperley [see access, May-June 1992] simulates complex systems with more atoms via the CM-5. This should be particularly useful for materials that exhibit both large- and small-scale quantum behavior. The Path Integral Monte Carlo code is now running on the CM-5 in the MIMD mode. Work on using this code to continue the simulation of hydrogen at high pressure has begun. Recently the Grand Challenge Allocation Committee granted 150,000 node hours on the CM-5 to continue this work.

Technology transfer

New computational methods are developed and then transferred from NCSA to the national materials science community by the Quantum Systems layer of NCSA's Applications Group, which Ceperley heads. In addition to his research, Ceperley provides a voice for materials scientists by defining the capabilities of NCSA's computational environment and determining allocations policy on NCSA architectures. Toward this end, NCSA has hosted a series of international long-term visitors and postdoctoral research associates.

Recent visitors include: Roberto Car [University of Geneva], Detlef Hohl [KFA (German national laboratory), JŸlich], Michel Cafferel [Toulouse], and Krauth [Paris]. UIUC postdoctoral associates at NCSA include: Silvia Bacci, Lubos Mitas, and Massimo Bonisegni.

Marcus Wagner, Jeff Grossman, William Magro, and Matt Jones--UIUC graduate research assistants at NCSA--are obtaining first-hand experience with new architectures and methods under Ceperley's guidance. Ceperley is currently participating in an effort within UIUC's College of Engineering to define a new Program in Computational Science and Engineering that will be designed to train students in applying supercomputers to scientific problems. Ceperley lectures extensively on algorithms at an annual workshop on new methods in QMC. Initiated by NCSA, this practice is now being perpetuated by the condensed matter community. Ceperley plans to give a tutorial on Monte Carlo methods at Physics Computing '93. In the fall of 1993, he will visit the University of Lausanne to further collaboration with Roberto Car on QMC methods.

With Jim Gubernatis (Los Alamos National Laboratory), Ceperley organized a workshop on ``Quantum Many-Body Computations for Condensed Matter Physics'' to be held in Santa Barbara, CA in spring 1994. It will be attended by colleagues Walter Kohn, Doug Scalopino, and Robert Sugar from Santa BarbaraÕs Institute of Theoretical Physics [see access, October-December 1992], as well as other national and international colleagues, including Malvin Kalos (director, Cornell Theory Center) and Car.

Only a start

Materials science is in its infancy. Ceperley points out, ``We're still very far from understanding how to solve the equations, but that's only part of the problem. The other part is the possible complexity. After all, even a person is a material. That's how complicated materials can be.

``Biological things are an example of something extremely complex that's just made from a few elements. You can take the elements, and you can mix them in an infinite number of ways. We won't exhaust this science for centuries-probably even millennia.''

Image Above: Results of a simulation of a surface layer of helium atoms on graphite. Because of quantum motion, the helium atoms are a probability cloud. The three atoms in the center of the picture are exchanging positions. This results in a ferromagnetic property: they become spin aligned at several thousandths of a degree above absolute zero. The work was done as part of a collaboration between Benard Bernu at the University of Paris and David Ceperley at NCSA. (Courtesy of David Ceperley)

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access / Spring 1993 / NCSA / pubs@ncsa.uiuc.edu