Felipe H. da Jornada

Meiyue Shao, Lin Lin, Chao Yang et al.

The single particle energies obtained in a Kohn--Sham density functional theory (DFT) calculation are generally known to be poor approximations to electron excitation energies that are measured in transport, tunneling and spectroscopic experiments such as photo-emission spectroscopy. The correction to these energies can be obtained from the poles of a single particle Green's function derived from a many-body perturbation theory. From a computational perspective, the accuracy and efficiency of such an approach depends on how a self energy term that properly accounts for dynamic screening of electrons is approximated. The $G_0W_0$ approximation is a widely used technique in which the self energy is expressed as the convolution of a non-interacting Green's function ($G_0$) and a screened Coulomb interaction ($W_0$) in the frequency domain. The computational cost associated with such a convolution is high due to the high complexity of evaluating $W_0$ at multiple frequencies. In this paper, we discuss how the cost of $G_0W_0$ calculation can be reduced by constructing a low rank approximation to the frequency dependent part of $W_0$. In particular, we examine the effect of such a low rank approximation on the accuracy of the $G_0W_0$ approximation. We also discuss how the numerical convolution of $G_0$ and $W_0$ can be evaluated efficiently and accurately by using a contour deformation technique with an appropriate choice of the contour.

Yanzhen Wang, Yiyang Jiang, Diana Golovanova et al.

We introduce QMBench, a comprehensive benchmark designed to evaluate the capability of large language model agents in quantum materials research. This specialized benchmark assesses the model's ability to apply condensed matter physics knowledge and computational techniques such as density functional theory to solve research problems in quantum materials science. QMBench encompasses different domains of the quantum material research, including structural properties, electronic properties, thermodynamic and other properties, symmetry principle and computational methodologies. By providing a standardized evaluation framework, QMBench aims to accelerate the development of an AI scientist capable of making creative contributions to quantum materials research. We expect QMBench to be developed and constantly improved by the research community.

Johnathan D. Georgaras, Akash Ramdas, Chung Hsuan Shan et al.

Twisted layered van-der-Waals materials often exhibit unique electronic and optical properties absent in their non-twisted counterparts. Unfortunately, predicting such properties is hindered by the difficulty in determining the atomic structure in materials displaying large moiré domains. Here, we introduce a split machine-learned interatomic potential and dataset curation approach that separates intralayer and interlayer interactions and significantly improves model accuracy -- with a tenfold increase in energy and force prediction accuracy relative to conventional models. We further demonstrate that traditional MLIP validation metrics -- force and energy errors -- are inadequate for moiré structures and develop a more holistic, physically-motivated metric based on the distribution of stacking configurations. This metric effectively compares the entirety of large-scale moiré domains between two structures instead of relying on conventional measures evaluated on smaller commensurate cells. Finally, we establish that one-dimensional instead of two-dimensional moiré structures can serve as efficient surrogate systems for validating MLIPs, allowing for a practical model validation protocol against explicit DFT calculations. Applying our framework to HfS2/GaS bilayers reveals that accurate structural predictions directly translate into reliable electronic properties. Our model-agnostic approach integrates seamlessly with various intralayer and interlayer interaction models, enabling computationally tractable relaxation of moiré materials, from bilayer to complex multilayers, with rigorously validated accuracy.

Meiyue Shao, Felipe H. da Jornada, Lin Lin et al.

We present a new structure preserving Lanczos algorithm for approximating the optical absorption spectrum in the context of solving full Bethe--Salpeter equation without Tamm--Dancoff approximation. The new algorithm is based on a structure preserving Lanczos procedure, which exploits the special block structure of Bethe--Salpeter Hamiltonian matrices. A recently developed technique of generalized averaged Gauss quadrature is incorporated to accelerate the convergence. We also establish the connection between our structure preserving Lanczos procedure with several existing Lanczos procedures developed in different contexts. Numerical examples are presented to demonstrate the effectiveness of our Lanczos algorithm.

Meiyue Shao, Felipe H. da Jornada, Chao Yang et al.

The Bethe-Salpeter eigenvalue problem is a dense structured eigenvalue problem arising from discretized Bethe-Salpeter equation in the context of computing exciton energies and states. A computational challenge is that at least half of the eigenvalues and the associated eigenvectors are desired in practice. We establish the equivalence between Bethe-Salpeter eigenvalue problems and real Hamiltonian eigenvalue problems. Based on theoretical analysis, structure preserving algorithms for a class of Bethe-Salpeter eigenvalue problems are proposed. We also show that for this class of problems all eigenvalues obtained from the Tamm-Dancoff approximation are overestimated. In order to solve large scale problems of practical interest, we discuss parallel implementations of our algorithms targeting distributed memory systems. Several numerical examples are presented to demonstrate the efficiency and accuracy of our algorithms.