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!
Study offers new theoretical approach to describing non-equilibrium phase transitions
27.04.2017 | DOE/Argonne National Laboratory
SwRI-led team discovers lull in Mars' giant impact history
26.04.2017 | Southwest Research Institute
More and more automobile companies are focusing on body parts made of carbon fiber reinforced plastics (CFRP). However, manufacturing and repair costs must be further reduced in order to make CFRP more economical in use. Together with the Volkswagen AG and five other partners in the project HolQueSt 3D, the Laser Zentrum Hannover e.V. (LZH) has developed laser processes for the automatic trimming, drilling and repair of three-dimensional components.
Automated manufacturing processes are the basis for ultimately establishing the series production of CFRP components. In the project HolQueSt 3D, the LZH has...
Reflecting the structure of composites found in nature and the ancient world, researchers at the University of Illinois at Urbana-Champaign have synthesized thin carbon nanotube (CNT) textiles that exhibit both high electrical conductivity and a level of toughness that is about fifty times higher than copper films, currently used in electronics.
"The structural robustness of thin metal films has significant importance for the reliable operation of smart skin and flexible electronics including...
The nearby, giant radio galaxy M87 hosts a supermassive black hole (BH) and is well-known for its bright jet dominating the spectrum over ten orders of magnitude in frequency. Due to its proximity, jet prominence, and the large black hole mass, M87 is the best laboratory for investigating the formation, acceleration, and collimation of relativistic jets. A research team led by Silke Britzen from the Max Planck Institute for Radio Astronomy in Bonn, Germany, has found strong indication for turbulent processes connecting the accretion disk and the jet of that galaxy providing insights into the longstanding problem of the origin of astrophysical jets.
Supermassive black holes form some of the most enigmatic phenomena in astrophysics. Their enormous energy output is supposed to be generated by the...
The probability to find a certain number of photons inside a laser pulse usually corresponds to a classical distribution of independent events, the so-called...
Microprocessors based on atomically thin materials hold the promise of the evolution of traditional processors as well as new applications in the field of flexible electronics. Now, a TU Wien research team led by Thomas Müller has made a breakthrough in this field as part of an ongoing research project.
Two-dimensional materials, or 2D materials for short, are extremely versatile, although – or often more precisely because – they are made up of just one or a...
20.04.2017 | Event News
18.04.2017 | Event News
03.04.2017 | Event News
27.04.2017 | Life Sciences
27.04.2017 | Physics and Astronomy
27.04.2017 | Earth Sciences