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  • Letter
  • Open Access

Variational method in relativistic quantum field theory without cutoff

Antoine Tilloy*

  • Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, 85748 Garching, Germany and Munich Center for Quantum Science and Technology (MCQST), Schellingstraße 4, D-80799 München, Germany

  • *antoine.tilloy@gmail.com
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Phys. Rev. D 104, L091904 – Published 11 November, 2021

DOI: https://doi.org/10.1103/PhysRevD.104.L091904

Abstract

The variational method is a powerful approach to solve many-body quantum problems nonperturbatively. However, in the context of relativistic quantum field theory, it needs to meet three seemingly incompatible requirements outlined by Feynman: extensivity, computability, and lack of UV sensitivity. In practice, variational methods break one of the three, which translates into the need to have an IR or UV cutoff. In this letter, I introduce a relativistic modification of continuous matrix product states that satisfies the three requirements jointly in 1+1 dimensions. I apply it to the self-interacting scalar field, without UV cutoff and directly in the thermodynamic limit. Numerical evidence suggests the error decreases faster than any power law in the number of parameters, while the cost remains only polynomial.

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Relativistic continuous matrix product states for quantum fields without cutoff

Antoine Tilloy
Phys. Rev. D 104, 096007 (2021)

Article Text

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Outline

Information

Phys. Rev. D 104, L091904– Published 11 November, 2021
  • Received 18 February 2021
  • Accepted 3 September 2021
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Open access publication funded by the Max Planck Society.

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