Bulletin of the American Physical Society
APS March Meeting 2023
Volume 68, Number 3
Las Vegas, Nevada (March 5-10)
Virtual (March 20-22); Time Zone: Pacific Time
Session N62: Quantum Embedding: Methods and ModelsFocus
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Sponsoring Units: DCOMP Chair: Cyrus Dreyer, Stony Brook University (SUNY) Room: Room 417 |
Wednesday, March 8, 2023 11:30AM - 12:06PM |
N62.00001: Invited Talk: Philipp WernerAb-initio GW+DMFT simulation of correlated materials Invited Speaker: Philipp Werner A proper ab-initio simulation of correlated electron materials requires a consistent description of correlations and screening. In quantum embedding approaches, this necessitates the self-consistent computation of the interaction parameters of the embedded system. A promising framework, which has been proposed 20 years ago [1], is the combination of the GW ab-initio method and dynamical mean field theory (DMFT). This fully diagrammatic scheme involves two coupled self-consistency loops for the Green's function and screened interaction, and requires the explicit treatment of dynamical screening effects. After the development of powerful impurity solvers for electron-boson systems [2], the first implementation of GW+DMFT for a single-band Hubbard model has been realized 10 years ago [3]. The method was subsequently extended into an ab-initio scheme for realistic materials simulations through the development of the multi-tier GW+DMFT approach [4,5]. This method employs a G0W0 downfolding to an intermediate energy space with O(10) bands. Within this intermediate space, correlations and screening are treated at the self-consistent GW level, while accurate local self-energies and polarizations for a subset of strongly correlated orbitals are obtained from (extended) DMFT calculations. Apart from the choice of the subspaces, multi-tier GW+DMFT is free of adjustable parameters, and thus provides a fully ab-initio description of correlated materials. Over the last years, the scheme has been extended to systems with multiple correlated atoms in the unit cell and successfully tested on a broad range of materials [6,7]. In this talk, I will give an overview of the methodological developments and the applications of the GW+DMFT framework. |
Wednesday, March 8, 2023 12:06PM - 12:18PM |
N62.00002: A quantum embedding approach to density-functional approximations for many-electron ensembles Filip Cernatic Density matrix embedding theory (DMET) [1] has recently been reformulated in terms of a unitary Householder transformation that is applied to a full-size (usually idempotent) ground-state one-electron reduced density matrix [2]. On that basis, a formally exact connection between DMET and density-functional theory (DFT) has been established for the Hubbard model [3]. In this context, the idempotency of the Kohn-Sham (KS) density matrix yields a closed embedding cluster made of as many bath orbitals as embedded fragment orbitals [4]. In this talk, an extension of the embedding procedure to bi-ensembles of ground and singly-excited states will be presented. In particular, we will show that, in spite of the non-idempotency of the ensemble KS density matrix, a closed (but enlarged) embedding cluster can still be designed through successive Householder transformations. Proof-of-concept results obtained with a finite one-dimensional Hubbard system will be shown. Extensions to higher excitations will also be discussed. |
Wednesday, March 8, 2023 12:18PM - 12:54PM |
N62.00003: Condensed Phase Chemical Physics from Full Cell Quantum Embedding Invited Speaker: Tianyu Zhu Quantitative first-principles description of spectral properties in strongly correlated materials remains a fundamental challenge in computational physics and chemistry. In this talk, I will describe a full cell quantum embedding framework to compute electronic charged excitations and spectra in correlated solids towards quantitative accuracy. First, I will introduce the basics of quantum embedding, particularly dynamical mean-field theory (DMFT), and discuss the strengths and challenges in previous formulations. Second, I will detail an ab initio all-orbital quantum embedding formulation that provides a new avenue for studying condensed phase chemical physics. I will demonstrate how molecular many-body quantum chemistry methods can be utilized for accurate description of photoemission spectra in a range of semiconducting, insulating, and metallic systems. Finally, a recent work on predicting characteristic temperature of Kondo effects will be discussed. |
Wednesday, March 8, 2023 12:54PM - 1:06PM |
N62.00004: Learning emergent models from ab initio many-body calculations Yueqing Chang, Lucas K Wagner The crucial step for understanding emergent low-energy physics is determining whether a particular model is emergent from ultraviolet physics. The state-of-the-art model derivation procedures, e.g., the constrained density functional theory and constrained random phase approximation, start from identifying a reduced Hilbert space using intuition and a given formulation of the effective models. While other methods, including the numerical renormalization group, do not require a priori information of the effective model but involve a choice of a logarithmic discretization scale on the spectrum and truncation of the Hilbert space by keeping the lowest-lying states. It would be preferable if the emergent degree of freedom could be learned without a priori knowledge using highly accurate many-body calculations since wave functions can be variationally improved. |
Wednesday, March 8, 2023 1:06PM - 1:18PM Author not Attending |
N62.00005: Determinantal Quantum Monte Carlo solver for Cluster Perturbation Theory Shuhan Ding, Edwin W Huang, Yao Wang, Jiarui Liu Cluster Perturbation Theory (CPT) is a technique for computing the spectral function of fermionic |
Wednesday, March 8, 2023 1:18PM - 1:30PM |
N62.00006: Convergence behavior of ghost rotationally-invariant slave-boson theory at small bath size: a comparative study with dynamical mean-field theory Tsung-Han Lee, Nicola Lanata, Gabriel Kotliar We study the convergence behavior of the ghost-rotationally-invariant slave-boson (gRISB) theory with increasing bath orbitals and compare it to the dynamical mean-field theory (DMFT) on the single-band Hubbard model. We show that the accuracy of gRISB can be systematically improved by increasing the number of ghost-orbitals in the bath of the embedded impurity model, similar to DMFT. Moreover, we demonstrate that gRISB generally produces more accurate static physical quantities than DMFT at small bath size, where the total energy and double occupancy in gRISB converge rapidly with bath size Nb = 3 while DMFT requires Nb = 5 to reach the same level of convergence. In addition, gRISB also captures reliable spectral functions compared to DMFT. Our results demonstrate that gRISB is a promising method that requires a few bath orbitals to reach convergence. |
Wednesday, March 8, 2023 1:30PM - 1:42PM |
N62.00007: Connections between tensor network influence functional and real-time density matrix embedding theory Gunhee Park, Nathan Ng, David Reichman, Garnet K Chan We develop connections between tensor network-based influence functional method and real-time density matrix embedding theory (DMET) for computing non-equilibrium electron dynamics in strongly correlated systems, specifically in non-equilibrium quantum impurity problems. In real-time DMET theory, the equation of motion is derived using the time-dependent variational principle. Here, we formulate tensor network method that can project bath degrees of freedom into finite degrees of discretized bath. We derive the equation of motion for the coupled impurity and bath wavefunction within the discretized bath using tensor network truncations. The numerical performance is compared in the quench dynamics of single impurity Anderson model. |
Wednesday, March 8, 2023 1:42PM - 1:54PM |
N62.00008: An efficient method for quantum impurity models in and out of equilibrium Julian Thoenniss, Alessio Lerose, Michael Sonner, Dmitry A Abanin Describing a quantum impurity coupled to non-interacting fermionic reservoirs is a paradigmatic problem in quantum many-body physics. We propose an approach to analyze impurity dynamics based on the matrix-product state (MPS) representation of the Feynman-Vernon influence functional (IF) which fully encodes the dynamical influence of the environment. The efficiency of the MPS representation rests on the moderate value of the temporal entanglement (TE) entropy of the IF, viewed as a fictitious “wave function” in the time domain. Once the IF is encoded by a MPS, local correlation functions can be efficiently computed for arbitrary impurity parameters. |
Wednesday, March 8, 2023 1:54PM - 2:06PM |
N62.00009: Quantum kernel machine learning of density functionals using a Levy-Lieb pure-state embedding Sri Chaitanya Das Pemmaraju, Amol Deshmukh We illustrate a framework for exact density functional theory using variational quantum circuits based on the constraint-search formulation of Levy and Lieb. Using the Hubbard dimer as a paradigmatic model, we discuss the implementation of explicit density variational energy minimization using a density-constrained variational quantum eigensolver approach [1]. Further, by interpreting the Levy-Lieb mapping from one-body densities to many-electron wavefunctions as a feature embedding into pure states we demonstrate a fidelity based quantum kernel for machine learning observable functionals of the ground-state density. We explore the ability of such a quantum kernel to generalize to unseen data through numerical experiments on the Hubbard dimer. |
Wednesday, March 8, 2023 2:06PM - 2:18PM |
N62.00010: A precise single particle density matrix functional for multi-orbital Mott physics via VDAT Zhengqian Cheng, Zhengqian Cheng, Chris A Marianetti The recently developed variational discrete action theory (VDAT) provides a systematic variational approach to the many-body problem, where the quality of the solution is regulated by an integer N, and increasing N monotonically approaches the exact solution. VDAT can be exactly evaluated in the d=∞ multi-orbital Hubbard model using the self-consistent canonical discrete action theory (SCDA), which requires a self-consistency condition of the integer time Green's functions. Previous work demonstrates that N=3 quantitatively captures multi-orbital Mott/Hund physics at a cost similar to the Gutzwiller approximation. Here we provide an analytic procedure to automatically satisfy the self-consistency condition of the SCDA at N=3, yielding an even more efficient algorithm with enhanced numerical stability. This analytic procedure provides a natural way to construct a single particle density matrix functional which captures Mott/Hund physics, and closed-form expressions are derived for the single band model at half filling. We present results and performance analysis for the five orbital Hubbard model in d=∞. The developments in this work will be important to applying VDAT at N=3 in strongly correlated electron materials. |
Wednesday, March 8, 2023 2:18PM - 2:30PM |
N62.00011: Analytic Continuation of Multipoint Correlation Functions: From Imaginary to Real Frequencies Johannes J Halbinger, Anxiang Ge, Seung-Sup B. Lee, Jan von Delft, Fabian B Kugler Conceptually, the Matsubara formalism (MF), using imaginary frequencies, and the Keldysh formalism (KF), formulated in real frequencies, give equivalent results for equilibrium systems which are invariant under time translations. While the MF is more convenient due to its reduced complexity compared to the KF, the computation of physical observables requires the analytical continuation of functions from imaginary to real frequencies. The analytic continuation is well-known for two-point correlation functions, but for general multipoint correlators, a straightforward recipe for obtaining all Keldysh components from the MF correlator had not been formulated yet. Recently a representation of MF and KF correlation functions in terms of formalism-independent partial spectral functions and formalism-specific kernels was introduced [1]. We use this representation to formally elucidate the connection between both formalisms and show how arbitrary multipoint MF correlation functions can be analytically continued to yield all Keldysh components of the corresponding KF correlation function, and illustrate this procedure explicitly for the Hubbard atom. |
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