Density matrix embedding theory (DMET) is a relatively new technique for the calculation of strongly correlated systems. Recently, block product DMET (BPDMET) was introduced for the study of spin systems such as the antiferromagnetic $J_1 - J_2$ model on the square lattice. In this paper, we extend the variational Ansatz of BPDMET using spin-state optimization, yielding improved results. We apply the same techniques to the Kitaev-Heisenberg model on the honeycomb lattice, comparing the results when using several types of clusters. Energy profiles and correlation functions are investigated. A diagonalization in the tangent space of the variational approach yields information on the excited states and the corresponding spectral functions.
A many-body wave function can be factorized in Fock space into a marginal amplitude describing a set of strongly correlated orbitals and a conditional amplitude for the remaining weakly correlated part. The marginal amplitude is the solution of a Schrödinger equation with an effective Hamiltonian that can be viewed as embedding the marginal wave function in the environment of weakly correlated electrons. Here, the complementary equation for the conditional amplitude is replaced by a generalized Kohn-Sham equation, for which an orbital-dependent functional approximation is shown to reproduce th…
We present a quantum embedding methodology to resolve the Anderson impurity model in the context of dynamical mean-field theory, based on an extended exact diagonalization method. Our method provides a maximally localized quantum impurity model, where the non-local components of the correlation potential remain minimal. This method comes at a large benefit, as the environment used in the quantum embedding approach is described by propagating correlated electrons and hence offers a polynomial increase $O(N^4)$ of the number of degrees of freedom for the embedding mapping without adding bath sit…
Neural-Network Quantum Embedding Solvers for Correlated Materials
Center for Computational Quantum Physics, Flatiron Institute（平顿研究所计算量子物理中心）；Collège de France（法兰西公学院）；CPHT, CNRS, Ecole Polytechnique, IP Paris（巴黎综合理工学院、法国国家科学研究中心、巴黎高等研究院）；DQMP, Université de Genève（日内瓦大学）；Department of Physics, Columbia University（哥伦比亚大学物理系）；Université Paris-Saclay, CNRS, CEA, Institut de Physique Théorique（巴黎萨克雷大学、法国国家科学研究中心、法国原子能和替代能源委员会、理论物理研究所）
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 calculati…
We present a multi-scale approach to efficiently embed an ab initio correlated chemical fragment described by its energy-weighted density matrices, and entangled with a wider mean-field many-electron system. This approach, first presented in Phys. Rev. B, 98, 235132 (2018), is here extended to account for realistic long-range interactions and broken symmetry states. The scheme allows for a systematically improvable description in the range of correlated fluctuations out of the fragment into the system, via a self-consistent optimization of a coupled auxiliary mean-field system. It is discussed…
Coherent cellular dynamical mean-field theory: a real-space quantum embedding approach to disorder in strongly correlated electron systems
Max-Planck-Institut für Festkörperforschung（马克斯·普朗克固体研究所）；Department of Physics, Columbia University（哥伦比亚大学物理系）；Center for Computational Quantum Physics, Flatiron Institute（平顿研究院计算量子物理中心）；Institute of Information Systems Engineering, TU Wien（维也纳工业大学信息系统工程学院）；Institute of Solid State Physics, TU Wien（维也纳工业大学固体物理研究所）；Department of Physics, Friedrich-Alexander-Universität Erlangen/Nürnberg（埃尔朗根-纽伦堡弗里德里希-亚历山大大学物理系）
The dynamical fluctuations in approaches such as dynamical mean-field theory (DMFT) allow for the self-consistent optimization of a local fragment, hybridized with a true correlated environment. We show that these correlated environmental fluctuations can instead be efficiently captured in a wave function perspective in a computationally cheap, frequency-independent, zero-temperature approach. This allows for a systematically improvable, short-time wave function analogue to DMFT, which entails a number of computational and numerical benefits. We demonstrate this approach to solve the correlate…
The accurate ab-initio simulation of periodic solids with strong correlations is one of the grand challenges of condensed matter. While mature methods exist for weakly correlated solids, the ab-initio description of strongly correlated systems is an active field of research. In this work, we show results for the single particle spectral function of the two correlated $d$-electron solids NiO and MnO from self-energy embedding theory. Unlike earlier work, the theory does not use any adjustable parameters and is fully ab-initio, while being able to treat both the strong correlation and the non-lo…
Quantum Monte Carlo assessment of embedding for for strongly correlated defects: interplay between mean-field starting point and interactions
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；University of California, Santa Barbara（加州大学圣塔芭芭拉分校）；Flatiron Institute（平顿研究所）；Bielefeld University（比勒费尔德大学）；Stony Brook University（石溪大学）
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 fun…
Quantum-Classical Embedding via Ghost Gutzwiller Approximation for Enhanced Simulations of Correlated Electron Systems
Ames National Laboratory（艾姆斯国家实验室）；Department of Physics and Astronomy, Iowa State University（爱荷华州立大学物理与天文系）；School of Electrical Engineering and Computer Science, Washington State University（华盛顿州立大学电气与计算机工程学院）；School of Physics and Astronomy, Rochester Institute of Technology（罗切斯特理工学院物理与天文学院）；Center for Computational Quantum Physics, Flatiron Institute（平顿研究所计算量子物理中心）
Exact ground-state for the periodic Anderson model in D=2 dimensions at finite value of the interaction and absence of the direct hopping in the correlated f-band
Density matrix embedding theory (DMET) formally requires the matching of density matrix blocks obtained from high-level and low-level theories, but this is sometimes not achievable in practical calculations. In such a case, the global band gap of the low-level theory vanishes, and this can require additional numerical considerations. We find that both the violation of the exact matching condition and the vanishing low-level gap are related to the assumption that the high-level density matrix blocks are non-interacting pure-state $v$-representable (NI-PS-V), which assumes that the low-level den…
We present a new quantum embedding theory called dynamical configuration interaction (DCI) that combines wave function and Green's function theories. DCI captures static correlation in a correlated subspace with configuration interaction and couples to high-energy, dynamic correlation outside the subspace with many-body perturbation theory based on Green's functions. In the correlated subspace, we use a wave function description to avoid embedding the two-particle vertex, which greatly simplifies the frequency structure of the embedding. DCI takes the strengths of both theories to balance stat…
