Mathematical tool helps calculate properties of quantum materials more
quickly

Date:
August 14, 2020
Source:
Helmholtz-Zentrum Berlin fu"r Materialien und Energie
Summary:
Many quantum materials have been nearly impossible to simulate
mathematically because the computing time required is too long. Now
engineers have demonstrated a way to considerably reduce the
computing time. This could accelerate the development of materials
for energy- efficient IT technologies of the future.



FULL STORY ==========================================================================
Many quantum materials have been nearly impossible to simulate
mathematically because the computing time required is too long. Now
engineers have demonstrated a way to considerably reduce the
computing time. This could accelerate the development of materials for energy-efficient IT technologies of the future.


========================================================================== Supercomputers around the world work around the clock on research
problems. In principle, even novel materials can be simulated in computers
in order to calculate their magnetic and thermal properties as well as
their phase transitions. The gold standard for this kind of modelling
is known as the quantum Monte Carlo method.

Wave-Particle Dualism However, this method has an intrinsic problem:
due to the physical wave- particle dualism of quantum systems, each
particle in a solid-state compound not only possesses particle-like
properties such as mass and momentum, but also wave-like properties
such as phase. Interference causes the "waves" to be superposed on each
other, so that they either amplify (add) or cancel (subtract) each other locally. This makes the calculations extremely complex.

It is referred to the sign problem of the quantum Monte Carlo method.

Minimisation of the problem "The calculation of quantum material characteristics costs about one million hours of CPU on mainframe
computers every day," says Prof. Jens Eisert, who heads the joint
research group at Freie Universita"t Berlin and the HZB. "This is a
very considerable proportion of the total available computing time."
Together with his team, the theoretical physicist has now developed
a mathematical procedure by which the computational cost of the sign
problem can be greatly reduced. "We show that solid-state systems can
be viewed from very different perspectives. The sign problem plays a
different role in these different perspectives. It is then a matter of
dealing with the solid-state system in such a way that the sign problem
is minimised," explains Dominik Hangleiter, first author of the study
that has now been published in Science Advances.

From simple spin systems to more complex ones For simple solid-state
systems with spins, which form what are known as Heisenberg ladders, this approach has enabled the team to considerably reduce the computational
time for the sign problem. However, the mathematical tool can also be
applied to more complex spin systems and promises faster calculation of
their properties.

"This provides us with a new method for accelerated development of
materials with special spin properties," says Eisert. These types of
materials could find application in future IT technologies for which data
must be processed and stored with considerably less expenditure of energy.


========================================================================== Story Source: Materials provided by Helmholtz-Zentrum_Berlin_fu"r_Materialien_und_Energie.

Note: Content may be edited for style and length.


========================================================================== Journal Reference:
1. Dominik Hangleiter, Ingo Roth, Daniel Nagaj, Jens Eisert. Easing the
Monte Carlo sign problem. Science Advances, 2020 DOI: 10.1126/
sciadv.abb8341 ==========================================================================

Link to news story: https://www.sciencedaily.com/releases/2020/08/200814163332.htm

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