Forum for Science, Industry and Business

Sponsored by:     3M 
Search our Site:


The uncalculability of electron systems

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
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
Dr. Olivia Meyer-Streng
Max Planck Institute of Quantum Optics
Press & Public Relations
Phone: +49 - 89 / 32905 213
Fax: +49 - 89 / 32905 200

Dr. Olivia Meyer-Streng | idw
Further information:

More articles from Physics and Astronomy:

nachricht Pulses of electrons manipulate nanomagnets and store information
21.07.2017 | American Institute of Physics

nachricht Vortex photons from electrons in circular motion
21.07.2017 | National Institutes of Natural Sciences

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: Manipulating Electron Spins Without Loss of Information

Physicists have developed a new technique that uses electrical voltages to control the electron spin on a chip. The newly-developed method provides protection from spin decay, meaning that the contained information can be maintained and transmitted over comparatively large distances, as has been demonstrated by a team from the University of Basel’s Department of Physics and the Swiss Nanoscience Institute. The results have been published in Physical Review X.

For several years, researchers have been trying to use the spin of an electron to store and transmit information. The spin of each electron is always coupled...

Im Focus: The proton precisely weighted

What is the mass of a proton? Scientists from Germany and Japan successfully did an important step towards the most exact knowledge of this fundamental constant. By means of precision measurements on a single proton, they could improve the precision by a factor of three and also correct the existing value.

To determine the mass of a single proton still more accurate – a group of physicists led by Klaus Blaum and Sven Sturm of the Max Planck Institute for Nuclear...

Im Focus: On the way to a biological alternative

A bacterial enzyme enables reactions that open up alternatives to key industrial chemical processes

The research team of Prof. Dr. Oliver Einsle at the University of Freiburg's Institute of Biochemistry has long been exploring the functioning of nitrogenase....

Im Focus: The 1 trillion tonne iceberg

Larsen C Ice Shelf rift finally breaks through

A one trillion tonne iceberg - one of the biggest ever recorded -- has calved away from the Larsen C Ice Shelf in Antarctica, after a rift in the ice,...

Im Focus: Laser-cooled ions contribute to better understanding of friction

Physics supports biology: Researchers from PTB have developed a model system to investigate friction phenomena with atomic precision

Friction: what you want from car brakes, otherwise rather a nuisance. In any case, it is useful to know as precisely as possible how friction phenomena arise –...

All Focus news of the innovation-report >>>



Event News

Closing the Sustainability Circle: Protection of Food with Biobased Materials

21.07.2017 | Event News

»We are bringing Additive Manufacturing to SMEs«

19.07.2017 | Event News

The technology with a feel for feelings

12.07.2017 | Event News

Latest News

NASA looks to solar eclipse to help understand Earth's energy system

21.07.2017 | Earth Sciences

Stanford researchers develop a new type of soft, growing robot

21.07.2017 | Power and Electrical Engineering

Vortex photons from electrons in circular motion

21.07.2017 | Physics and Astronomy

More VideoLinks >>>