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Solvers for the Hermitian and the pseudo-Hermitian Bethe-Salpeter equation in the Yambo code: Implementation and Performance

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Petru Milev, Blanca Mellado-Pinto, Muralidhar Nalabothula, Ali Esquembre Kucukalic, Fernando Alvarruiz, Enrique Ramos, Francesco Filippone, Alejandro Molina-Sanchez
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Ludger Wirtz, Jose E. Roman, Davide Sangalli

Materials Science · Submitted 14 Apr 2025

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Our results demonstrate that it is now feasible to handle dense BSE matrices of the order of 10^5.

how it is stated · asserted 0.98 read the record →

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arXiv ID2504.10096 (version 3)
Pith IDHMRZAQ43, Pith's permanent record of this paper and its review
CitationAlejandro Molina-Sanchez, Ali Esquembre Kucukalic, Blanca Mellado-Pinto, Davide Sangalli, Enrique Ramos, Fernando Alvarruiz, Francesco Filippone, Jose E. Roman, Ludger Wirtz, Muralidhar Nalabothula, Petru Milev. "Solvers for the Hermitian and the pseudo-Hermitian Bethe-Salpeter equation in the Yambo code: Implementation and Performance." arXiv:2504.10096 (2025). https://pith.science/paper/HMRZAQ43
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,908 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.14 · human participants 0.01 · controlled comparison 0.12 · randomized assignment 0.01 · states quantitative result 0.91 · compares with prior results 0.66 · mentions code or data availability 0.05.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; .

We analyze the performance of two strategies in solving the structured eigenvalue problem deriving from the Bethe-Salpeter equation (BSE) in condensed matter physics. The BSE matrix is constructed with the Yambo code, and the two strategies are implemented by interfacing Yambo with the ScaLAPACK and ELPA libraries for direct diagonalization, and with the SLEPc library for the iterative approach. We consider both the Hermitian (Tamm-Dancoff approximation) and pseudo-Hermitian forms, addressing dense matrices of three different sizes. A description of the implementation is also provided, with details for the pseudo-Hermitian case. Timing and memory utilization are analyzed on both CPU and GPU clusters. Our results demonstrate that it is now feasible to handle dense BSE matrices of the order of 10^5.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We analyze the performance of two strategies in solving the structured eigenvalue problem deriving from the Bethe-Salpeter equation (BSE) in condensed matter physics. contribution 0.98 0.87 0.05 asserted 0.81
s1 The BSE matrix is constructed with the Yambo code, and the two strategies are implemented by interfacing Yambo with the ScaLAPACK and ELPA libraries for direct diagonalization, and with the SLEPc library for the iterative approach. method 1.00 0.89 0.03 asserted 1.00
s2 We consider both the Hermitian (Tamm-Dancoff approximation) and pseudo-Hermitian forms, addressing dense matrices of three different sizes. method 0.85 0.87 0.04 asserted 0.85
s3 A description of the implementation is also provided, with details for the pseudo-Hermitian case. method 0.76 0.78 0.03 asserted 0.97
s4 Timing and memory utilization are analyzed on both CPU and GPU clusters. method 0.94 0.92 0.04 asserted 0.89
s5 Our results demonstrate that it is now feasible to handle dense BSE matrices of the order of 10^5. result 0.76 0.94 0.83 asserted 0.98

What kind of paper the classifier reports this is: method or tool 0.81 · evidence from simulation or computation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

We analyze the performance of two strategies in solving the structured eigenvalue problem deriving from the Bethe-Salpeter equation (BSE) in condensed matter physics. The BSE matrix is constructed with the Yambo code, and the two strategies are implemented by interfacing Yambo with the ScaLAPACK and ELPA libraries for direct diagonalization, and with the SLEPc library for the iterative approach. We consider both the Hermitian (Tamm-Dancoff approximation) and pseudo-Hermitian forms, addressing dense matrices of three different sizes. A description of the implementation is also provided, with details for the pseudo-Hermitian case. Timing and memory utilization are analyzed on both CPU and GPU clusters. Our results demonstrate that it is now feasible to handle dense BSE matrices of the order of 10^5.

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