• Open Access

Solving the Bethe-Salpeter equation with exponential convergence

Markus Wallerberger, Hiroshi Shinaoka, and Anna Kauch
Phys. Rev. Research 3, 033168 – Published 20 August 2021

Abstract

The Bethe-Salpeter equation plays a crucial role in understanding the physics of correlated fermions, relating to optical excitations in solids as well as resonances in high-energy physics. Yet, it is notoriously difficult to control numerically, typically requiring an effort that scales polynomially with energy scales and accuracy. This puts many interesting systems out of computational reach. Using the intermediate representation and sparse modeling for two-particle objects on the Matsubara axis, we develop an algorithm that solves the Bethe-Salpeter equation in O(L8) time with O(L4) memory, where L grows only logarithmically with inverse temperature, bandwidth, and desired accuracy. This opens the door for computations in hitherto inaccessible regimes. We benchmark the method on the Hubbard atom and on the multiorbital weak-coupling limit, where we observe the expected exponential convergence to the analytical results. We then showcase the method for a realistic impurity problem.

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  • Received 10 December 2020
  • Accepted 23 July 2021

DOI:https://doi.org/10.1103/PhysRevResearch.3.033168

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.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied PhysicsParticles & Fields

Authors & Affiliations

Markus Wallerberger1,*, Hiroshi Shinaoka2,*, and Anna Kauch1

  • 1Institute of Solid State Physics, TU Wien, 1040 Vienna, Austria
  • 2Department of Physics, Saitama University, Saitama 338-8570, Japan

  • *These authors contributed equally to this work.

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Vol. 3, Iss. 3 — August - October 2021

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