Forum for Science, Industry and Business

Sponsored by:     3M 
Search our Site:

 

UMass Amherst theoretical physicists find a way to simulate strongly correlated fermions

19.03.2012
New technique could open the door to practical superconductor applications, as well as to solving difficult 'many-body' problems in high-energy physics, condensed matter and ultra-cold atoms

Combining known factors in a new way, theoretical physicists Boris Svistunov and Nikolai Prokof'ev at the University of Massachusetts Amherst, with three alumni of their group, have solved an intractable 50-year-old problem: How to simulate strongly interacting quantum systems to allow accurate predictions of their properties.

It could open the door to practical superconductor applications, as well as to solving difficult "many-body" problems in high-energy physics, condensed matter and ultra-cold atoms.

The theoretical breakthrough by Prokof'ev and Svistunov at UMass Amherst, with their alumni Kris Van Houcke now at Ghent University, Felix Werner at Ecole Normale Supérieure Paris and Evgeny Kozik at Ecole Polytechnique, is reported in the current issue of Nature Physics. The paper also includes crucial results of an experimental validation conducted by Martin Zwierlein and colleagues at MIT.

Svistunov says, "The accompanying experiment is a breakthrough on its own because achieving a few percent accuracy has long been a dream in the field of ultra-cold atoms. We needed this confirmation from Mother Nature."

Van Houcke adds, "Our answers and the experimental results perfectly agree. This is important because in physics you can always make a prediction, but unless it is controlled, with narrow error bars, you're basically just gambling. Our new method makes accurate predictions."

Physicists have long been able to numerically simulate statistical behavior of bosonic systems by mapping them onto polymers in four dimensions, as Richard Feynman proposed in the 1950s. "In a bosonic liquid one typically wants to know at what temperature the superfluid phase transition occurs," Prokof'ev explains, "and mapping onto the polymers yields an essentially exact answer."

But simulating particle behavior in strongly interacting fermionic liquids, like strongly interacting electrons in high-temperature superconducting compounds, has been devilishly elusive, he adds. "The polymer trick does not work here because of the notorious negative-sign problem, a hallmark of fermionic statistics."

Apart from mapping onto the polymers, Feynman proposed yet another solution, in terms of "diagrams" now named after him. These Feynman diagrams are graphical expressions for serial expansion of Green's functions, a mathematical tool that describes statistical properties of each unique system. Feynman diagrams were never used for making quantitatively accurate predictions for strongly interacting systems because people believed that evaluating and summing all of them was simply impossible, Svistunov points out. But the UMass Amherst team now has found a way to do this.

What they discovered is a trick—called Diagrammatic Monte Carlo—of sampling the Feynman series instead of calculating diagrams one by one. Especially powerful is the Bold Diagrammatic Monte Carlo (BDMC) scheme. This deals with a partially summed Feynman series (Dyson's development) in which the diagrams are constructed not from the bare Green's functions of non-interacting system (usually represented by thin lines), but from the genuine Green's functions of the strongly interacting system being looked for (usually represented by bold lines).

"We poll a series of integrals, and the result is fed back to the series to keep improving our knowledge of the Green's function," says Van Houcke, who developed the BDMC code over the past three years.

The BDMC protocol works a bit like sampling to predict the outcome of an election but with the difference that results of polling are being constantly fed back to the "electorate," Prokof'ev and Svistunov add. "We repeat this with several hundred processors over several days until the solution converges. That is, the Green's function doesn't change anymore. And once you know the Green's function, you know all the basic thermodynamic properties of the system. This has never been done before."

Janet Lathrop | EurekAlert!
Further information:
http://www.umass.edu

Further reports about: BDMC Diagrammatic Nature Immunology ionic liquid ultra-cold atoms

More articles from Physics and Astronomy:

nachricht Astronomers find unexpected, dust-obscured star formation in distant galaxy
24.03.2017 | University of Massachusetts at Amherst

nachricht Gravitational wave kicks monster black hole out of galactic core
24.03.2017 | NASA/Goddard Space Flight Center

All articles from Physics and Astronomy >>>

The most recent press releases about innovation >>>

Die letzten 5 Focus-News des innovations-reports im Überblick:

Im Focus: Giant Magnetic Fields in the Universe

Astronomers from Bonn and Tautenburg in Thuringia (Germany) used the 100-m radio telescope at Effelsberg to observe several galaxy clusters. At the edges of these large accumulations of dark matter, stellar systems (galaxies), hot gas, and charged particles, they found magnetic fields that are exceptionally ordered over distances of many million light years. This makes them the most extended magnetic fields in the universe known so far.

The results will be published on March 22 in the journal „Astronomy & Astrophysics“.

Galaxy clusters are the largest gravitationally bound structures in the universe. With a typical extent of about 10 million light years, i.e. 100 times the...

Im Focus: Tracing down linear ubiquitination

Researchers at the Goethe University Frankfurt, together with partners from the University of Tübingen in Germany and Queen Mary University as well as Francis Crick Institute from London (UK) have developed a novel technology to decipher the secret ubiquitin code.

Ubiquitin is a small protein that can be linked to other cellular proteins, thereby controlling and modulating their functions. The attachment occurs in many...

Im Focus: Perovskite edges can be tuned for optoelectronic performance

Layered 2D material improves efficiency for solar cells and LEDs

In the eternal search for next generation high-efficiency solar cells and LEDs, scientists at Los Alamos National Laboratory and their partners are creating...

Im Focus: Polymer-coated silicon nanosheets as alternative to graphene: A perfect team for nanoelectronics

Silicon nanosheets are thin, two-dimensional layers with exceptional optoelectronic properties very similar to those of graphene. Albeit, the nanosheets are less stable. Now researchers at the Technical University of Munich (TUM) have, for the first time ever, produced a composite material combining silicon nanosheets and a polymer that is both UV-resistant and easy to process. This brings the scientists a significant step closer to industrial applications like flexible displays and photosensors.

Silicon nanosheets are thin, two-dimensional layers with exceptional optoelectronic properties very similar to those of graphene. Albeit, the nanosheets are...

Im Focus: Researchers Imitate Molecular Crowding in Cells

Enzymes behave differently in a test tube compared with the molecular scrum of a living cell. Chemists from the University of Basel have now been able to simulate these confined natural conditions in artificial vesicles for the first time. As reported in the academic journal Small, the results are offering better insight into the development of nanoreactors and artificial organelles.

Enzymes behave differently in a test tube compared with the molecular scrum of a living cell. Chemists from the University of Basel have now been able to...

All Focus news of the innovation-report >>>

Anzeige

Anzeige

Event News

International Land Use Symposium ILUS 2017: Call for Abstracts and Registration open

20.03.2017 | Event News

CONNECT 2017: International congress on connective tissue

14.03.2017 | Event News

ICTM Conference: Turbine Construction between Big Data and Additive Manufacturing

07.03.2017 | Event News

 
Latest News

Argon is not the 'dope' for metallic hydrogen

24.03.2017 | Materials Sciences

Astronomers find unexpected, dust-obscured star formation in distant galaxy

24.03.2017 | Physics and Astronomy

Gravitational wave kicks monster black hole out of galactic core

24.03.2017 | Physics and Astronomy

VideoLinks
B2B-VideoLinks
More VideoLinks >>>