Quantum Breakthrough: Feynman Diagram Sampling and Feedback

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Quantum mechanics is the most accurate (and strangest) theory in the history of physics. Yet it has great difficulty making accurate predictions for “many-body” systems — those involving a large number of particles. Physicists Nikolai Prokof’ev and Boris Svistunov at the University of Massachusetts Amherst with three alumni of their group propose a novel solution: random sampling of Feynman diagrams with feedback to converge on the answer. Experiment results confirm the accuracy of this innovative approach.

Feynman Diagrams

This theoretical breakthrough is reported in the current issue of Nature Physics. The team, led by Prokof’ev and Svistunov, also includes alumni Kris Van Houcke now at Ghent University, Felix Werner at Ecole Normale Supérieure Paris and Evgeny Kozik at Ecole Polytechnique.

Feynman Diagram – Electron / Positron Annihilation – Image by bitwise

At the heart of the Prokof’ev/Svistunov method are Feynman diagrams, pioneered by Richard Feynman in 1948. Each diagram depicts a possible way quantum events could occur. (And represents the mathematics of the process.)  However, “the events represented by a diagram are virtual,” Svistunov told Decoded Science, “since they cannot be verified by experiment. Only the sum of all diagrams is physically meaningful.”

To see how this works, imagine an electron at point A. What are the odds that this single particle will be detected at point B some distance away at a certain time? The sum of all Feynman diagrams gives the probability of finding the electron at B. This strange and counter-intuitive approach accurately predicts the statistical behavior of “a few electrons in simple circumstances,” wrote Feynman in his book QED, The Strange Theory of Light and Matter.

But calculating the huge number of possible Feynman diagrams in “strongly-interacting” quantum systems — those involving a large number of interacting particles — has proven extremely difficult in most cases.

Fermions, Bosons, and Spin

Spin is a measure of the angular momentum of a particle. Fermions are particles with half-integer spin — such as electrons and other matter particles. They have a spin of 1/2.  Bosons, on the other hand, have integer spin, such as photons, which have a spin of 1. All force-carrier particles are bosons. Composite particles, atomic nuclei, and atoms are fermions if they contain an odd number of fermion particles.

In the past, physicists have found impressive success modeling bosons in many-body experiments by mapping them into polymers in 4-D using the sum-of-all-paths approach. This method, however, has not worked for fermions — due to the infamous minus sign problem. “This increases noise dramatically, ” Svistunov told Decoded Science, “requiring such an enormous number of samples that calculations become impossible.”

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