Forum for Science, Industry and Business

Sponsored by:     3M 
Search our Site:

 

The uncalculability of electron systems

24.08.2009
Theoretical physicists of the Max Planck Institute of Quantum Optics reveal limitations of Density Functional Theory using Quantum Information Theory tools.

The electric and magnetic properties of solids are impossible to calculate exactly: The complex interactions of the many electrons which underly these phenomena cannot be computed even by the most powerful classical computers. Here, the central task is to determine the ground state of the electrons moving in the field of the positively charged nuclei.

The most widely used method for treating such systems is Density Functional Theory, which reduces the many-body problem to a single particle interaction. As Dr. Norbert Schuch, scientist in the theory division of Prof. Ignacio Cirac at the Max Planck Institute of Quantum Optics in Garching, and Prof. Frank Verstraete from the University of Vienna, report in Nature Physics (DOI: 10.1038/NPHYS1370), there exist however fundamental limitations to the applicability of this theory. The scientists succeeded by using methods developed in Quantum Information Theory, demonstrating that these methods can give deep insights beyond the development of quantum computers.

One of the central problems in quantum mechanics is to determine the ground state of a complex system consisting of many interacting electrons. An example taken from chemistry is the geometry of large molecules: the spatial arrangement of the atoms in the molecule is the one for which the energy of the electrons moving in the field of the nuclei is minimized. Thus, by determining the ground state of the electrons one can infer the three-dimensional structure of the molecule. The same holds for solids: Their electric and magnetic properties, including exotic phenomena such as high-temperature superconductivity, ultimately originate from the motion of the electrons in the periodic potential of the positively charged nuclei.

Density Functional Theory (DFT) makes use of the fact that the complex interaction of the electrons is the same in all these cases and encapsulates it in some kind of "black box", the so-called "universal functional". By using this functional, every many-electron problem can in principle be rephrased as a single-particle problem which can then be solved relatively easily. The challenge consists in finding this functional, and in practice, often more specific problem-dependent approximations are being used.

In their work, Schuch and Verstraete investigate the limits of the applicability of DFT: Is it possible to find this universal functional which would considerably simplify the treatment of many-electron systems - or are there fundamental bounds which prohibit this? To this end, they use methods of quantum complexity theory, a subarea of quantum information science, which aims at classifying problems according to their difficulty, especially concerning the question whether they can be efficiently solved by quantum computers. Whereas e.g. quantum computers can often simulate the time evolutions of quantum systems efficiently, computing ground states of complex quantum systems poses a hard problem even for a quantum computer.

In their work, Schuch and Verstraete prove on the one hand that ground states of many-electron systems are hard to compute even for quantum computers. On the contrary, they show that these problems can be solved efficiently even by classical computers using Density Functional Theory, given the universal functional is known. This shows that in these cases it is fundamentally impossible to compute the functional and explains the need for more specific approximations. This exhibits that despite its broad applicability, there are fundamental limitations to Density Functional Theory.

[Olivia Meyer-Streng/Norbert Schuch]

Original publication:
Norbert Schuch and Frank Verstraete
"Computational Complexity of interacting electrons and fundamental limitations
of Density Functional Theory"
Nature Physics, Advance Online Publication, DOI: 10.1038/NPHYS1370
Contact:
Dr. Norbert Schuch
Max Planck Institute of Quantum Optics
Theory Division
Hans-Kopfermann-Straße 1
85748 Garching
Phone: +49 - 89 / 32905 105
Fax: +49 - 89 / 32905 200
E-mail: norbert.schuch@mpq.mpg.de
Dr. Olivia Meyer-Streng
Max Planck Institute of Quantum Optics
Press & Public Relations
Phone: +49 - 89 / 32905 213
Fax: +49 - 89 / 32905 200
E-mail: olivia.meyer-streng@mpq.mpg.de

Dr. Olivia Meyer-Streng | idw
Further information:
http://www.mpq.mpg.de

More articles from Physics and Astronomy:

nachricht Igniting a solar flare in the corona with lower-atmosphere kindling
29.03.2017 | New Jersey Institute of Technology

nachricht NASA spacecraft investigate clues in radiation belts
28.03.2017 | 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: A Challenging European Research Project to Develop New Tiny Microscopes

The Institute of Semiconductor Technology and the Institute of Physical and Theoretical Chemistry, both members of the Laboratory for Emerging Nanometrology (LENA), at Technische Universität Braunschweig are partners in a new European research project entitled ChipScope, which aims to develop a completely new and extremely small optical microscope capable of observing the interior of living cells in real time. A consortium of 7 partners from 5 countries will tackle this issue with very ambitious objectives during a four-year research program.

To demonstrate the usefulness of this new scientific tool, at the end of the project the developed chip-sized microscope will be used to observe in real-time...

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...

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

Researchers shoot for success with simulations of laser pulse-material interactions

29.03.2017 | Materials Sciences

Igniting a solar flare in the corona with lower-atmosphere kindling

29.03.2017 | Physics and Astronomy

As sea level rises, much of Honolulu and Waikiki vulnerable to groundwater inundation

29.03.2017 | Earth Sciences

VideoLinks
B2B-VideoLinks
More VideoLinks >>>