arXiv subjects

Chia-Nan Yeh

Publications and source records attributed to Chia-Nan Yeh.

At least 19 recordsLinked to original sources

arXiv2026

Self-consistent vertex corrected $GW$ with static and dynamic screening using tensor hypercontraction: assessment of molecular charged excitations

We investigate self-consistent vertex corrections to the $GW$ self-energy for ionization potentials (IPs) and electron affinities (EAs). We benchmark IPs against $Δ$CCSD(T) references in the $G_0W_0Γ$29 and GW100 sets and compare GW100 EAs with EOM-CCSD references. Because many anions are metastable, these addition energies are model quantities and should not be interpreted as experimental EAs. Tensor hypercontraction (THC) of the Coulomb integrals enables efficient self-consistent $GWΓ_Σ$ implementations, where vertex corrections are included only in the self-energy. We establish a hierarchy of vertex-corrected self-energies relative to sc$GW$, ordered from least to most negative as SOX $>$ SOSEX $>$ G3W2 $>$ 2SOSEX $>$ sc$GW$. Equivalently, the absolute magnitude increases along this sequence. This trend follows an effective-screening picture, in which increasing screening progressively reduces exchange contributions. Static and dynamic variants show consistent differences due to the frequency dependence of the screened interaction. Across all methods, vertex corrections act as an approximately frequency-uniform self-energy renormalization rather than altering its spectral structure. In terms of accuracy, sc$GWΓ_Σ$ does not uniformly improve IPs or the EA model quantities over sc$GW$. For IPs, SOX and SOSEX usually degrade performance, whereas 2SOSEX and G3W2 remain close to sc$GW$, with only marginal improvements for selected systems at higher cost. Although the tested variants reduce EA MAEs, this should not be interpreted as a general improvement for physical anions because many nominal EA states are metastable. These results indicate that generic vertex insertions are insufficient to outperform sc$GW$; systematic improvements require designed diagrammatic approximations combined with efficient tensor factorization.

cond-mat.str-el↗

arXiv2026

Importance of effective Coulomb interactions for $T_c$ in cuprates

Cuprate superconductors exhibit the highest observed superconducting $T_c$ at atmospheric pressure. However, the magnitude of $T_c$ varies significantly between different cuprates. At present, it is unclear what properties of the crystal structure affect $T_c$ most strongly, yet such an understanding must underpin any efforts toward high-$T_c$ materials design. To address this issue, we perform a large scale systematic study, employing a combination of data collection, state-of-the-art numerical methods, and statistical analysis. We identify about 40 different cuprate compounds, and we compile detailed data about their $T_c$'s and crystal structures from literature and the available databases. Using a fully automated procedure, for each compound we compute the DFT bandstructure and downfold it to two of the most commonly studied low-energy lattice models, namely the single-band Hubbard and the three-band Emery models. The downfolding is based on the approach of MLWFs and cRPA. Finally, we apply a thorough and unbiased statistical analysis to investigate the correlations between the experimentally measured $T_c$'s and the computed parameters of our theoretical models. Our data indicates that more sophisticated models might be needed to describe all cuprates on the same footing. Nevertheless, we find that $T_c$ scales well with simple functions of model parameters. We confirm a previously observed trend that $t'$ in the single-band model correlates with the experimental $T_c$, and we find that $T_c$ appears to vanish below a finite value of $t'$, in agreement with recent ground-state calculations for the Hubbard model. However, we find that the coupling strength also plays a role: throughout our entire dataset, $T_c$ correlates the most with the Coulomb coupling on the $p$-orbitals in the 3-band model, highlighting the importance of the oxygen sites in the copper-oxide planes.

cond-mat.str-el↗

arXiv2026

The Python Simulations of Chemistry Framework: 10 years of an open-source quantum chemistry project

Over the past decade, the Python-based Simulations of Chemistry Framework (PySCF) has developed into a widely used open-source platform for electronic structure theory and quantum chemical method development. This article reviews the major advances since the previous overview in 2020, covering new modules and methodology, infrastructure changes, and performance benchmarks.

physics.chem-ph↗

arXiv2026

Electronic correlations and dynamical screening with ab initio quantum embedding

First-principles descriptions of correlated quantum materials require a simultaneous treatment of strong local many-body effects and nonlocal dynamical screening. We present an efficient fully self-consistent implementation of $GW$+EDMFT that combines nonlocal effects at the $GW$ level with a non-perturbative treatment of local correlations within extended dynamical mean-field theory (EDMFT), while providing a controlled double-counting prescription. Crucially, self-consistency in both the Green's function and the dynamically screened interaction is essential to achieve a consistent description of screening processes across energy scales. The efficient computation of this self-consistent solution is enabled here by compressing two-particle correlation functions using interpolative separable density fitting (ISDF). Applying the scheme to the Mott insulator SrMnO$_3$ and the correlated metal LaNiO$_3$, we show that full self-consistency resolves the overscreening inherent to constrained-RPA approaches. By suppressing spurious low-energy screening channels, a Mott-insulating state in quantitative agreement with experiment is obtained for SrMnO$_3$. These results establish fully self-consistent $GW$+EDMFT as a predictive ab initio framework for strongly correlated quantum materials.

cond-mat.str-el↗

arXiv2026

Interpolative separable density fitting on adaptive real space grids

We generalize the interpolative separable density fitting (ISDF) method, used for compressing the four-index electron repulsion integral (ERI) tensor, to incorporate adaptive real space grids for potentially highly localized single-particle basis functions. To do so, we employ a fast adaptive algorithm, the recently-introduced dual-space multilevel kernel-splitting method, to solve the Poisson equation for the ISDF auxiliary basis functions. The adaptive grids are generated using a high-order accurate, black-box procedure that satisfies a user-specified error tolerance. Our algorithm relies on the observation, which we prove, that an adaptive grid resolving the pair densities appearing in the ERI tensor can be straightforwardly constructed from one that resolves the single-particle basis functions, with the number of required grid points differing only by a constant factor. We find that the ISDF compression efficiency for the ERI tensor with highly localized basis sets is comparable to that for smoother basis sets compatible with uniform grids. To demonstrate the performance of our procedure, we consider several molecular systems with all-electron basis sets which are intractable using uniform grid-based methods. Our work establishes a pathway for scalable many-body electronic structure simulations with arbitrary smooth basis functions, making simulations of phenomena like core-level excitations feasible on a large scale.

physics.comp-ph↗

arXiv2024

Tensor hypercontraction for self-consistent vertex corrected GW with static and dynamic screening; applications to molecules and solids with superexchange

For molecules and solids, we developed efficient MPI-parallel algorithms for evaluating the second-order exchange term with bare, statically screened, and dynamically screened interactions. We employ the resulting term in a fully self-consistent manner together with scGW, resulting in the following vertex-corrected scGW schemes: scGWSOX, scGWSOSEX, scGW2SOSEX, and scG3W2theories. We show that for the vertex evaluation, the reduction of scaling by tensor hypercontraction (THC) has two limiting execution regimes. We used the resulting code to perform the largest (by the number of orbitals) fully self-consistent calculations with the SOX term. We demonstrate that our procedure allows for a reliable evaluation of even small energy differences. Utilizing a broken-symmetry approach, we explore the influence of the SOX term on the effective magnetic exchange couplings. We show that the treatment of SOX has a significant impact on the obtained values of the effective exchange constants, which we explain through a self-energy dependence on an effective dielectric constant. We confirm this explanation by analyzing natural orbitals and local changes in charge transfer quantifying superexchange. Our analysis explains the structure of weak electron correlation responsible for the modulation of superexchange in both molecules and solids. Finally, for solids, we evaluate Neel temperatures utilizing the high-temperature expansion and compare the results obtained with experimental measurements.

cond-mat.str-el↗

arXiv2024

Green/WeakCoupling: Implementation of fully self-consistent finite-temperature many-body perturbation theory for molecules and solids

The accurate ab initio simulation of molecules and periodic solids with diagrammatic perturbation theory is an important task in quantum chemistry, condensed matter physics, and materials science. In this article, we present the WeakCoupling module of the open-source software package Green, which implements fully self-consistent diagrammatic weak coupling simulations, capable of dealing with real materials in the finite-temperature formalism. The code is licensed under the permissive MIT license. We provide self-consistent GW (scGW) and self-consistent second-order Green's function perturbation theory (GF2) solvers, analysis tools, and post-processing methods. This paper summarizes the theoretical methods implemented and provides background, tutorials and practical instructions for running simulations.

cond-mat.mtrl-sci↗

arXiv2024

Tensor hypercontraction for fully self-consistent imaginary-time GF2 and GWSOX methods: theory, implementation, and role of the Green's function second-order exchange for intermolecular interactions

We apply tensor hypercontraction (THC) to reduce the computational scaling of expensive fully self-consistent Green's function methods. We present an efficient MPI-parallel algorithm and its implementation for evaluating the correlated second-order exchange term (SOX). This approach enabled us to conduct the largest fully self-consistent calculations with over 1100 atomic orbitals (AOs), with negligible errors attributed to THC fitting. Utilizing our THC implementation for scGW, scGF2, and scGWSOX (GW plus the SOX term iterated to achieve full Green's function self-consistency), we evaluated energies of intermolecular interactions. This approach allowed us to circumvent issues related to reference dependence and ambiguity in energy evaluation, which are common challenges in non-self-consistent calculations. We demonstrate that scGW exhibits a slight overbinding tendency for large systems, contrary to the underbinding observed with non-self-consistent RPA. Conversely, scGWSOX exhibits a slight underbinding tendency for such systems. This behavior is both physical and systematic and is caused by exclusion-principle violating diagrams or corresponding corrections. Our analysis elucidates the role played by these different diagrams, which is crucial for the construction of rigorous, accurate, and systematic methods. Finally, we explicitly show that all perturbative fully self-consistent Green's function methods are size-extensive.

physics.chem-ph↗

arXiv2024

Low-Scaling algorithms for $GW$ and constrained random phase approximation using symmetry-adapted interpolative separable density fitting

We present low-scaling algorithms for $GW$ and constrained random phase approximation based on a symmetry-adapted interpolative separable density fitting (ISDF) procedure that incorporates the space-group symmetries of crystalline systems. The resulting formulations scale cubically with respect to system sizes and linearly with the number of $\mathbf{k}$-points, regardless of the choice of single-particle basis and whether a quasiparticle approximation is employed. We validate these methods through comparisons with published literature and demonstrate their efficiency in treating large-scale systems through the construction of downfolded many-body Hamiltonians for carbon dimer defects embedded in hexagonal boron nitride supercells. Our work highlights the efficiency and general applicability of ISDF in the context of large-scale many-body calculations with $\mathbf{k}$-point sampling beyond density functional theory.

cond-mat.mtrl-sci↗

arXiv2023

Low-Scaling Algorithm for the Random Phase Approximation using Tensor Hypercontraction with k-point Sampling

We present a low-scaling algorithm for the random phase approximation (RPA) with \textbf{k}-point sampling in the framework of tensor hypercontraction (THC) for electron repulsion integrals (ERIs). The THC factorization is obtained via a revised interpolative separable density fitting (ISDF) procedure with a momentum-dependent auxiliary basis for generic single-particle Bloch orbitals. Our formulation does not require pre-optimized interpolating points nor auxiliary bases, and the accuracy is systematically controlled by the number of interpolating points. The resulting RPA algorithm scales linearly with the number of \textbf{k}-points and cubically with the system size without any assumption on sparsity or locality of orbitals. The errors of ERIs and RPA energy show rapid convergence with respect to the size of the THC auxiliary basis, suggesting a promising and robust direction to construct efficient algorithms of higher-order many-body perturbation theories for large-scale systems.

cond-mat.mtrl-sci↗

arXiv2022

Triple excitations in Green's function coupled cluster solver for studies of strongly correlated systems in the framework of self-energy embedding theory

Embedding theories became important approaches used for accurate calculations of both molecules and solids. In these theories, a small chosen subset of orbitals is treated with an accurate method, called an impurity solver, capable of describing higher correlation effects. Ideally, such a chosen fragment should contain multiple orbitals responsible for the chemical and physical behavior of the compound. Handing a large number of chosen orbitals presents a very significant challenge for the current generation of solvers used in the physics and chemistry community. Here, we develop a Green's function coupled cluster singles doubles and triples (GFCCSDT) solver that can be used for a quantitative description in both molecules and solids. This solver allows us to treat orbital spaces that are inaccessible to other accurate solvers. At the same time, GFCCSDT maintains high accuracy of the resulting self-energy. Moreover, in conjunction with the GFCCSD solver, it allows us to test the systematic convergence of computational studies. Developing the CC family of solvers paves the road to fully systematic Green's function embedding calculations in solids. In this paper, we focus on the investigation of GFCCSDT self-energies for a strongly correlated problem of SrMnO$_3$ solid. Subsequently, we apply this solver to solid MnO showing that an approximate variant of GFCCSDT is capable of yielding a high accuracy orbital resolved spectral function.

physics.chem-ph↗

arXiv2022

Fully Self-Consistent Finite-Temperature $GW$ in Gaussian Bloch Orbitals for Solids

We present algorithmic and implementation details for the fully self-consistent finite-temperature $GW$ method in Gaussian Bloch orbitals for solids. Our implementation is based on the finite-temperature Green's function formalism in which all equations are solved on the imaginary axis, without resorting to analytical continuation during the self-consistency. No quasiparticle approximation is employed and all matrix elements of the self-energy are explicitly evaluated. The method is tested by evaluating the band gaps of selected semiconductors and insulators. We show agreement with other, differently formulated finite-temperature sc$GW$ implementations when finite-size corrections and basis set errors are taken into account. By migrating computationally intensive calculations to GPUs, we obtain scalable results on large supercomputers with nearly optimal performance. Our work demonstrates the applicability of Gaussian orbital based sc$GW$ for $\emph{ab initio}$ correlated materials simulations and provides a sound starting point for embedding methods built on top of $GW$.

cond-mat.mtrl-sci↗

arXiv2022

Relativistic Self-Consistent $GW$: Exact Two-Component Formalism with One-Electron Approximation for Solids

We present a formulation of relativistic self-consistent $GW$ for solids based on the exact two-component formalism with one-electron approximation (X2C1e) and non-relativistic Coulomb interactions. Our theory allows us to study scalar relativistic effects, spin-orbit coupling, and the interplay of relativistic effects with electron correlation without adjustable parameters. Our all-electron implementation is fully $ab$ $initio$ and does not require a pseudopotential constructed from atomic calculations. We examine the effect of the X2C1e approximation by comparison to the established four-component formalism and reach excellent agreement. The simplicity of X2C1e enables the construction of higher order theories, such as embedding theories, on top of perturbative calculations.

cond-mat.str-el↗

arXiv2021

Iterative subspace algorithms for finite-temperature solution of Dyson equation

One-particle Green's functions obtained from the self-consistent solution of the Dyson equation can be employed in evaluation of spectroscopic and thermodynamic properties for both molecules and solids. However, typical acceleration techniques used in the traditional quantum chemistry self-consistent algorithms cannot be easily deployed for the Green's function methods, because of non-convex grand potential functional and non-idempotent density matrix. Moreover, the inclusion of correlation effects in the form of the self-energy matrix and changing chemical potential or fluctuations in the number of particles can make the optimization problem more difficult. In this paper, we study acceleration techniques to target the self-consistent solution of the Dyson equation directly. We use the direct inversion in the iterative subspace (DIIS), the least-squared commutator in the iterative subspace (LCIIS), and the Krylov space accelerated inexact Newton method (KAIN). We observe that the definition of the residual has a significant impact on the convergence of the iterative procedure. Based on the Dyson equation, we generalize the concept of the commutator residual used in DIIS (CDIIS) and LCIIS, and compare it with the difference residual used in DIIS and KAIN. The commutator residuals outperform the difference residuals for all considered molecular and solid systems within both GW and GF2. The generalized CDIIS and LCIIS methods successfully converged restricted GF2 calculations for a number of strongly correlated systems, which could not be converged before. We also provide practical recommendations to guide convergence in such pathological cases.

physics.chem-ph↗

arXiv2021

Exploring Coupled Cluster Green's function as a method for treating system and environment in Green's function embedding methods

Within the self-energy embedding theory (SEET) framework, we study coupled cluster Green's function (GFCC) method in two different contexts: as a method to treat either the system or environment present in the embedding construction. Our study reveals that when GFCC is used to treat the environment we do not see improvement in total energies in comparison to the coupled cluster method itself. To rationalize this puzzling result, we analyze the performance of GFCC as an impurity solver with a series of transition metal oxides. These studies shed light on strength and weaknesses of such a solver and demonstrate that such a solver gives very accurate results when the size of the impurity is small. We investigate if it is possible to achieve a systematic accuracy of the embedding solution when we increase the size of the impurity problem. We found that in such a case, the performance of the solver worsens, both in terms of finding the ground state solution of the impurity problem as well as the self-energies produced. We concluded that increasing the rank of GFCC solver is necessary to be able to enlarge impurity problems and achieve a reliable accuracy. We also have shown that natural orbitals from weakly correlated perturbative methods are better suited than symmetrized atomic orbitals (SAO) when the total energy of the system is the target quantity.

physics.chem-ph↗

arXiv2021

Analytical Continuation of Matrix-Valued Functions: Carathéodory Formalism

Finite-temperature quantum field theories are formulated in terms of Green's functions and self-energies on the Matsubara axis. In multi-orbital systems, these quantities are related to positive semidefinite matrix-valued functions of the Carathéodory and Schur class. Analysis, interpretation and evaluation of derived quantities such as real-frequency response functions requires analytic continuation of the off-diagonal elements to the real axis. We derive the criteria under which such functions exist for given Matsubara data and present an interpolation algorithm that intrinsically respects their mathematical properties. For small systems with precise Matsubara data, we find that the continuation exactly recovers all off-diagonal and diagonal elements. In real-materials systems, we show that the precision of the continuation is sufficient for the analytic continuation to commute with the Dyson equation, and we show that the commonly used truncation of off-diagonal self-energy elements leads to considerable approximation artifacts. Our method paves the way for the systematic evaluation of Matsubara data with equations of many-body theory on the real-frequency axis.

cond-mat.str-el↗

arXiv2021

Electron correlations in cubic paramagnetic perovskite Sr(V,Mn)O$_{3}$ -- Results from fully self-consistent self-energy embedding calculations

In this work, we use the thermodynamically consistent and conserving self-energy embedding theory (SEET) to study the spectra of the prototypical undistorted cubic perovskites SrVO$_3$ and SrMnO$_3$. In the strongly correlated metallic SrVO$_3$ we find that the usual attribution of the satellite peaks at -1.8eV to Hund or Hubbard physics in the $t_{2g}$ orbitals is inconsistent with our calculations. In the strongly correlated insulator SrMnO$_3$ we recover insulating behavior due to a feedback effect between the strongly correlated orbitals and the weakly correlated environment. Our calculation shows a systematic convergence of spectral features as the space of strongly correlated orbitals is enlarged, paving the way to a systematic parameter free study of correlated perovskites.

cond-mat.str-el↗

arXiv2021

Evaluation of two-particle properties within finite-temperature self-consistent one-particle Green's function methods: theory and application to GW and GF2

One-particle Green's function methods can model molecular and solid spectra at zero or non-zero temperatures. One-particle Green's functions directly provide electronic energies and one-particle properties, such as dipole moment. However, the evaluation of two-particle properties, such as $\langle{S^2}\rangle$ and $\langle{N^2}\rangle$ can be challenging, because they require a solution of the computationally expensive Bethe--Salpeter equation to find two-particle Green's functions. We demonstrate that the solution of the Bethe--Salpeter equation can be complitely avoided. Applying the thermodynamic Hellmann--Feynman theorem to self-consistent one-particle Green's function methods, we derive expressions for two-particle density matrices in a general case and provide explicit expressions for GF2 and GW methods. Such density matrices can be decomposed into an antisymmetrized product of correlated one-electron density matrices and the two-particle electronic cumulant of the density matrix. Cumulant expressions reveal a deviation from ensemble representability for GW, explaining its known deficiencies. We analyze the temperature dependence of $\langle{S^2}\rangle$ and $\langle{N^2}\rangle$ for a set of small closed-shell systems. Interestingly, both GF2 and GW show a non-zero spin contamination and a non-zero fluctuation of the number of particles for closed-shell systems at the zero-temperature limit.

physics.chem-ph↗