New numerical algorithms for old problems
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New numerical algorithms for old problems

Quantum field theories are of paramount importance in our understanding of the fundamental constituents of matter and their interactions: their study represents a cornerstone of contemporary research, ranging from high-energy particle physics to condensed-matter physics. However, describing their quantum many-body behavior is an extremely challenging task. Despite more than fifty years of developments of numerical and analytical methods to study these systems and numerous great achievements, many fundamental phenomena are still beyond reach of Monte Carlo methods, the most powerful numerical tool used to investigate these systems when no analytical solutions are available.

A paper published on Nature Communication this week by the Quantum Theory group of the Physics and Astronomy department of Padova University, presents a leap forward paving the way to the study of phenomena precluded before, introducing efficient numerical algorithms for investigating lattice gauge theories in the realistic scenario of three spatial dimensions.
The work considers complex mathematical structures, Tensor Networks, and for the first time, generalize them showing that tensor network methods provide a computational efficient description of the low- energy behavior of quantum field theories in three dimensions, such as quantum electrodynamics. By exploiting sophisticated algorithms they study how electrons and positrons organizes themselves in the different regimes in scenarios precluded before, overcoming the so-called “sign-problem” that curses Monte Carlo methods in some regimes. They observe some intriguing quantum phenomena completely counterintuitive in the “classical” world, such as the instability of the vacuum with respect to the spontaneous creation of particles and antiparticles and the peculiar behaviors of the interaction potential between two charges that changes its shape according to the strength of quantum interactions, called “confinement”.
These results show for the first time the potential of tensor network methods to the study of realistic quantum field theories, opening new perspective on the connection between high-energy phenomena and entanglement theory, the latter being at the basis of tensor network methods. These findings could stimulate the application of these strategies to processes of interest in particle physics and challenging open problems that are at the center of theoretical and experimental research efforts, such as the mechanism of quark confinement in the context of the Standard Model.


“Lattice quantum electrodynamics in (3+1)-dimensions at finite density with tensor networks” – «Nature Communications» – 2021
Giuseppe Magnifico, Timo Felser, Pietro Silvi & Simone Montangero

Press release, University of Padova, 17th of June 2021