Bulletin of the American Physical Society
APS March Meeting 2022
Volume 67, Number 3
Monday–Friday, March 14–18, 2022; Chicago
Session M49: Precision Many-Body Physics V: New Algorithms
8:00 AM–11:00 AM,
Wednesday, March 16, 2022
Room: McCormick Place W-471B
Sponsoring
Unit:
DCOMP
Chair: Hansveer Singh, University of Massachusetts, Amherst
Abstract: M49.00009 : Sparse-modeling solver for dynamical two-particle response of correlated electrons
10:24 AM–10:36 AM
Presenter:
Hiroshi Shinaoka
(Saitama Univ)
Authors:
Hiroshi Shinaoka
(Saitama Univ)
Markus Wallerberger
(Vienna Univ of Technology)
Anna Kauch
(Vienna Univ of Technology)
In this talk, we propose an efficient method for computing the dynamical susceptibility in DMFT. The proposed method extensively uses sparse-modeling techniques, including the intermediate representation [1,2], sparse sampling of vertex functions [3], and sparse convolution techniques for solving BSE [4]. The computational complexity of the proposed method scales only logarithmically with inverse temperature (apart from solving an impurity model).
We numerically demonstrate the efficiency of the method for the Hubbard model near its magnetic transition. First, we show that the local full vertex can be measured on sparse sampling frequencies using the recently proposed improved estimators [5] based on the continuous-time hybridization expansion quantum Monte Carlo method [6]. Then, we solve the BSE using a "sparse-modeling" BSE solver, which computes the dynamical susceptibility at finite bosonic Matsubara frequencies without using a cutoff for fermionic frequencies. We will first present results for the single-orbital Hubbard model on the square lattice. If time allows, we will also show preliminary results for more realistic multi-orbital models.
[1] H. Shinaoka et al., PRB 96, 035147 (2017).
[2] H. Shinaoka et al., arXiv:2106.12685.
[3] H. Shinaoka et al., SciPost Phys. 8, 012 (2020).
[4] M. Wallerberger*, H. Shinaoka*, A. Kauch, PRR 3, 033168 (2021).
[5] J. Kaufmann et al., PRB 96, 035114 (2017).
[6] P. Werner et al., PRL 97, 076405 (2006).
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