Robust analytic continuation of Green's functions via projection, pole estimation, and semidefinite relaxation

We present a machine learning (ML) framework for predicting Green's functions of molecular systems, from which photoemission spectra and quasiparticle energies at quantum many-body level can be obtained. Kernel ridge regression is adopted to predict self-energy matrix elements on compact imaginary frequency grids from static and dynamical mean-field electronic features, which gives direct access to real-frequency many-body Green's functions through analytic continuation and Dyson's equation. Feature and self-energy matrices are represented in a symmetry-adapted intrinsic atomic orbital plus projected atomic orbital basis to enforce rotational invariance. We demonstrate good transferability and high data efficiency of the proposed ML method across molecular sizes and chemical species by showing accurate predictions of density of states (DOS) and quasiparticle energies at the level of many-body perturbation theory (GW) or full configuration interaction. For the ML model trained on 48 out of 1995 molecules randomly sampled from the QM7 and QM9 data sets, we report the mean absolute errors of ML-predicted highest occupied and lowest unoccupied molecular orbital energies to be 0.13 and 0.10 eV, respectively, compared to GW@PBE0. We further showcase the capability of this method by applying the same ML model to predict DOS for significantly larger organic molecules with up to 44 heavy atoms.

Section: Resultsmentioning

confidence: 99%

“…More robust AC methods will be tested in the future. 85 To be consistent with FCI, we used full Dyson inversion for GW@HF in this section.…”

Section: Water Monomersmentioning

confidence: 99%

Machine Learning Many-Body Green’s Functions for Molecular Excitation Spectra

Venturella,

Hillenbrand,

et al. 2023

“…The conventional noise generation scheme relies on the analytic continuation of the correlation function to the complex plane. Such methods suffer from noncausality and nonphysical artifacts due to the numerical instability of many rational approximation schemes. , Here, we present a stable noise generation scheme that does not rely on the interpolation of any correlation function.…”

Section: Methodsmentioning

confidence: 99%

“…Such methods suffer from noncausality and nonphysical artifacts due to the numerical instability of many rational approximation schemes. 55,56 Here, we present a stable noise generation scheme that does not rely on the interpolation of any correlation function. We first rewrite the noise term as follows…”

Section: Noise Generationmentioning

confidence: 99%

Stochastic Schrödinger Equation Approach to Real-Time Dynamics of Anderson–Holstein Impurities: An Open Quantum System Perspective

Huang,

Xu,

Zhou

2024

Self Cite

We develop a stochastic Schrödinger equation (SSE) framework to simulate the real-time dynamics of Anderson–Holstein (AH) impurities coupled to a continuous Fermionic bath. The bath degrees of freedom are incorporated through fluctuating terms determined by exact system-bath correlations, which is derived in an ab initio manner. We show that such an SSE treatment provides a middle ground between numerically expansive microscopic simulations and macroscopic master equations. Computationally, the SSE model enables efficient numerical methods for propagating stochastic trajectories. We demonstrate that this approach not only naturally provides microscopically detailed information unavailable from reduced models but also captures effects beyond master equations, thus serving as a promising tool to study open quantum dynamics emerging in physics and chemistry.

“…No QP approximation is evoked to evaluate the spectral quantities in our version of sc GW . To yield spectral information, the finite-temperature Green’s function from the imaginary axis is continued to the real frequency axis with the help of the Nevanlinna analytical continuation technique introduced by Fei et al. , The spectral function can be derived from the continued Green’s function as scriptG ( i ω ) → a n a l y t i c a l .25em c o n t i n u a t i o n normalN normale normalv normala normaln normall normali normaln normaln normala A ( ω ) = prefix− 1 π I m { normalT normalr false[ G ( ω ) false] } …”

Section: Theorymentioning

confidence: 96%

Comparing Self-Consistent GW and Vertex-Corrected G₀W₀ (G₀W₀Γ) Accuracy for Molecular Ionization Potentials

Wen,

Abraham,

Harsha

et al. 2024

We test the performance of self-consistent GW and several representative implementations of vertex-corrected G 0 W 0 (G 0 W 0 Γ). These approaches are tested on benchmark data sets covering full valence spectra (first ionization potentials and some inner valence shell excitations). For small molecules, when comparing against state-of-the-art wave function techniques, our results show that full self-consistency in the GW scheme either systematically outperforms vertexcorrected G 0 W 0 or gives results of at least comparative quality. Moreover, G 0 W 0 Γ results in additional computational cost when compared to G 0 W 0 or self-consistent GW. The dependency of G 0 W 0 Γ on the starting mean-field solution is frequently more dominant than the magnitude of the vertex correction itself. Consequently, for molecular systems, self-consistent GW performed on the imaginary axis (and then followed by modern analytical continuation techniques) offers a more reliable approach to make predictions of ionization potentials.