Bridging applied math and quantum many-body physics and beyond via tensor methods

Seminar iTHEMS Theoretical Physics Seminar
Date
July 23 (Wed) 16:00 - 17:00, 2025 (JST)
Speaker
  • Hiroshi Shinaoka (Associate Professor, Department of Physics, Saitama University)
Venue
Language
English
Host
Masazumi Honda

In modern physics, high-dimensional functions and operators naturally arise in a wide range of contexts, including turbulence simulations, parameter-dependent partial differential equations (PDEs), and quantum field theory. Efficient representations and computations with such high-dimensional objects pose major challenges across disciplines.
Dimensionality reduction techniques such as the Quantics Tensor Train (QTT) [1] and Tensor Cross Interpolation (TCI) [2] were originally developed in applied mathematics. In our work, we have extended these methods to quantum many-body problems, demonstrating their effectiveness in handling complex high-dimensional structures in theoretical physics [3–10].
Given their generality, QTT and TCI are expected to find applications beyond quantum theory itself, in fields such as statistical field theory, model reduction, and control of complex systems, where similar high-dimensional structures emerge.
This presentation will first review the computational bottlenecks that arise in quantum many-body simulations and other high-dimensional problems. Then, we will introduce QTT and TCI from a broader, method-oriented perspective, aiming to bridge applied mathematics and quantum theoretical physics.

References

  1. I. V. Oseledets, Doklady, Math. 80, 653 (2009)
  2. I. V. Oseledets, SIAM Journal on Scientific Computing 33, 2295 (2011)
  3. H. Shinaoka, M. Wallerberger, Y. Murakami, K. Nogaki, R. Sakurai, P. Werner, A. Kauch, Phys. Rev. X 13, 021015 (2023)
  4. M. K. Ritter, Y. Núñez-Fernández, M. Wallerberger, J. von Delft, H. Shinaoka, X. Waintal, Phys. Rev. Lett. 132, 056501 (2024)
  5. Y. Núñez-Fernández, M. Jeannin, P. T. Dumitrescu, T. Kloss, J. Kaye, O. Parcollet, X. Waintal, Phys. Rev. X 12, 041018 (2022)
  6. Y. Núñez-Fernández, M. K. Ritter, M. Jeannin, J.-W. Li, T. Kloss, T. Louvet, S. Terasaki, O. Parcollet, J. von Delft, H. Shinaoka, X. Waintal, SciPost Phys. 18, 104 (2025)
  7. S. Rohshap, M. K. Ritter, H. Shinaoka, J. von Delft, M. Wallerberger, A. Kauch, Phys. Rev. Research 7, 023087 (2025)
  8. H. Ishida, N. Okada, S. Hoshino, H. Shinaoka, arXiv: 2405.06440
  9. M. Murray, H. Shinaoka, P. Werner, Phys. Rev. B 109, 165135 (2024)
  10. M. Środa, K. Inayoshi, H. Shinaoka, P. Werner, High-resolution nonequilibrium GW calculations based on quantics tensor trains, arXiv: 2412.14032

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