Sparse-modeling solver for dynamical two-particle response of correlated electrons
ORAL
Abstract
Computing dynamical two-particle response functions of correlated materials is a grand challenge in the field of computational material science. The dynamical mean-field theory (DMFT) is one of the most successful theories for computing one-particle response of correlated electrons. Nevertheless, it is notoriously difficult to compute two-particle responses as it involves solving the Bethe-Salpeter equation (BSE), whose computational effort scales unfavourably with inverse temperature and the number of bands.
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).
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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Presenters
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Hiroshi Shinaoka
Saitama Univ
Authors
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Hiroshi Shinaoka
Saitama Univ
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Markus Wallerberger
Vienna Univ of Technology
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Anna Kauch
Vienna Univ of Technology