We investigate the performance of Green's function coupled cluster singles and doubles (CCSD) method as a solver for Green's function embedding methods. To develop an efficient CC solver, we construct the one-particle Green's function from the coupled cluster (CC) wave function based on a non-hermitian Lanczos algorithm. The major advantage of this method is that its scaling does not depend on the number of frequency points. We have tested the applicability of the CC Green's function solver in the weakly to strongly correlated regimes by employing it for a half-filled 1D Hubbard model projected onto a single site impurity problem and a half-filled 2D Hubbard model projected onto a 4-site impurity problem. For the 1D Hubbard model, for all interaction strengths, we observe an excellent agreement with the full configuration interaction (FCI) technique, both for the self-energy and spectral function. For the 2D Hubbard, we have employed an open-shell version of the current implementation and observed some discrepancies from FCI in the strongly correlated regime. Finally, on an example of a small ammonia cluster, we analyze the performance of the Green's function CCSD solver within the self-energy embedding theory (SEET) with Hartee-Fock (HF) and Green's function second order (GF2) for the treatment of the environment.
We describe the use of coupled-cluster theory as an impurity solver in dynamical mean-field theory (DMFT) and its cluster extensions. We present numerical results at the level of coupled-cluster theory with single and double excitations (CCSD) for the density of states and self-energies of cluster impurity problems in the one- and two-dimensional Hubbard models. Comparison to exact diagonalization shows that CCSD produces accurate density of states and self-energies at a variety of values of $U/t$ and filling fractions. However, the low cost allows for the use of many bath sites, which we defi…
We apply the Green's function coupled cluster singles and doubles (GFCCSD) impurity solver to realistic impurity problems arising for strongly correlated solids within the self-energy embedding theory (SEET) framework. We describe the details of our GFCC solver implementation, investigate its performance, and highlight potential advantages and problems on examples of impurities created during the self-consistent SEET for antiferromagnetic MnO and paramagnetic SrMnO$_{3}$. GFCCSD provides satisfactory descriptions for weakly and moderately correlated impurities with sizes that are intractable b…
Tree tensor network impurity solver based on Cayley-tree mapping
Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）
We describe an open-source implementation of the continuous-time hybridization-expansion quantum Monte Carlo method for impurity models with general instantaneous two-body interactions and complex hybridization functions. The code is built on the ALPS libraries (Applications and Libraries for Physics Simulations).
We present an impurity solver based on adaptively truncated Hilbert spaces. The solver is particularly suitable for dynamical mean-field theory in circumstances where quantum Monte Carlo approaches are ineffective. It exploits the sparsity structure of quantum impurity models, in which the interactions couple only a small subset of the degrees of freedom. We further introduce an adaptive truncation of the particle or hole excited spaces, which enables computations of Green functions with an accuracy needed to avoid unphysical (sign change of imaginary part) self-energies. The method is benchma…
A reformulation of site-occupation embedding theory (SOET) in terms of Green's functions is presented. Referred to as site-occupation--Green's function embedding theory (SOGET), this novel extension of density-functional theory for model Hamiltonians shares many features with dynamical mean-field theory (DMFT) but is formally exact (in any dimension). In SOGET, the impurity-interacting correlation potential becomes a density-functional self-energy which is frequency-dependent and in principle non-local. A simple local density-functional approximation (LDA) combining the Bethe Ansatz (BA) LDA w…
We present a numerically exact Inchworm Monte Carlo method for equilibrium multiorbital quantum impurity problems with general interactions and hybridizations. We show that the method, originally developed to overcome the dynamical sign problem in certain real-time propagation problems, can also overcome the sign problem as a function of temperature for equilibrium quantum impurity models. This is shown in several cases where the current method of choice, the continuous-time hybridization expansion, fails due to the sign problem. Our method therefore enables simulations of impurity problems as…
In the present paper, we present an efficient continuous-time quantum Monte Carlo impurity solver with high acceptance rate at low temperature for multi-orbital quantum impurity models with general interaction. In this hybridization expansion impurity solver, the imaginary time evolution operator for the high energy multiplets, which decays very rapidly with the imaginary time, is approximated by a probability normalized $δ$-function. As the result, the virtual charge fluctuations of $f^{n}\rightarrow f^{n\pm1}$ are well included on the same footing without applying Schrieffer-Wolff transforma…
Multi-orbital quantum impurity models with general interaction and hybridization terms appear in a wide range of applications including embedding, quantum transport, and nanoscience. However, most quantum impurity solvers are restricted to a few impurity orbitals, discretized baths, diagonal hybridizations, or density-density interactions. Here, we generalize the inchworm quantum Monte Carlo method to the interaction expansion and explore its application to typical single- and multi-orbital problems encountered in investigations of impurity and lattice models. Our implementation generically ou…
Using an imaginary-time matrix-product state (MPS) based quantum impurity solver we perform a realistic dynamical mean-field theory (DMFT) calculation combined with density functional theory (DFT) for Sr$_2$RuO$_4$. We take the full Hubbard-Kanamori interactions and spin-orbit coupling (SOC) into account. The MPS impurity solver works at essentially zero temperature in the presence of SOC, a regime of parameters currently inaccessible to continuous-time quantum Monte Carlo (CTQMC) methods, due to a severe sign problem. We show that earlier results obtained at high temperature, namely that the …
In this paper, we present a new version of the $i$QIST software package, which is capable of solving various quantum impurity models by using the hybridization expansion (or strong coupling expansion) continuous-time quantum Monte Carlo algorithm. In the revised version, the software architecture is completely redesigned. New basis (intermediate representation or singular value decomposition representation) for the single-particle and two-particle Green's functions is introduced. A lot of useful physical observables are added, such as the charge susceptibility, fidelity susceptibility, Binder …
Recently solvers for the Anderson impurity model (AIM) working directly on the real-frequency axis have gained much interest. A simple and yet frequently used impurity solver is exact diagonalization (ED), which is based on a discretization of the AIM bath degrees of freedom. Usually, the bath parameters cannot be obtained directly on the real-frequency axis, but have to be determined by a fit procedure on the Matsubara axis. In this work we present an approach where the bath degrees of freedom are first discretized directly on the real-frequency axis using a large number of bath sites ($\appr…
In the dynamics of driven impurity models, there is a fundamental asymmetry between the processes of emission and absorption of environment excitations: most of the emitted excitations are rapidly and irreversibly scattered away, and only a small amount of them is reabsorbed back. We propose to use a stochastic simulation of the irreversible quantum emission processes in real-time dynamics, while taking into account the reabsorbed virtual excitations by the bath discretization. The resulting method delivers a fast convergence with respect to the number of bath sites, on a wide time interval, w…
We extend a previously proposed rotation and truncation scheme to optimize quantum Anderson impurity calculations with exact diagonalization [PRB 90, 085102 (2014)] to density-matrix renormalization group (DMRG) calculations. The method reduces the solution of a full impurity problem with virtually unlimited bath sites to that of a small subsystem based on a natural impurity orbital basis set. The later is solved by DMRG in combination with a restricted-active-space truncation scheme. The method allows one to compute Green's functions directly on the real frequency or time axis. We critically …
Neural network impurity solver for real-frequency dynamical mean-field theory
Suzhou Institute for Advanced Research, University of Science and Technology of China（中国科学技术大学苏州高等研究院）；School of Artificial Intelligence and Data Science, University of Science and Technology of China（中国科学技术大学人工智能与数据科学学院）；National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University（南京大学固体微结构物理实验室和物理系）；Collaborative Innovation Center of Advanced Microstructures, Nanjing University（南京大学先进微结构协同创新中心）
We present a tree tensor-network impurity solver suited for general multiorbital systems. The network is constructed to efficiently capture the entanglement structure and symmetry of an impurity problem. The solver works directly on the real-time/frequency axis and generates spectral functions with energy-independent resolution of the order of one percent of the correlated bandwidth. Combined with an optimized representation of the impurity bath, it efficiently solves self-consistent dynamical mean-field equations and calculates various dynamical correlation functions for systems with off-diag…
Although several impurity solvers in the dynamical mean field theory (DMFT) have been proposed, especially in multi-band systems, there are practical difficulties arising from a trade-off between numerical costs and reliability. In this study, we re-interpret the iterative perturbation theory (IPT) as an approximation which captures the strong correlation effects by mimicking the particular frequency structures of the exact full vertex, and extend it such that it can have efficiency and reliability simultaneously by modifying IPT vertex using the parquet equations. We apply this method to seve…
We present a quantum impurity solver based on a pseudo-particle framework, which combines diagrammatic resummations for a three-point vertex with diagrammatic Monte Carlo sampling of a four-point vertex. This recently proposed approach [A. J. Kim et al., arXiv:2112.15549] is generalized here to fermionic impurity problems and we discuss the technical details of the implementation, including the time-stepping approach, the Monte Carlo updates, and the routines for checking the two-particle irreducibility of the four-point vertex. We also explain how the vertex information can be efficiently sto…
