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arXiv:1803.01564 · The Journal of Chemical Physics

Band structures in coupled-cluster singles-and-doubles Green’s function (GFCCSD)

Yoritaka Furukawa, Taichi Kosugi, Hirofumi Nishi, Yu‐ichiro Matsushita

Published May 25, 2018• 23 citations
arXivHTMLPDF

Abstract

We demonstrate that the coupled-cluster singles-and-doubles Green's function (GFCCSD) method is a powerful and prominent tool drawing the electronic band structures and the total energies, which many theoretical techniques struggle to reproduce. We have calculated single-electron energy spectra via the GFCCSD method for various kinds of systems, ranging from ionic to covalent and van der Waals, for the first time: the one-dimensional LiH chain, one-dimensional C chain, and one-dimensional Be chain. We have found that the bandgap becomes narrower than in HF due to the correlation effect. We also show that the band structures obtained from the GFCCSD method include both quasiparticle and satellite peaks successfully. Besides, taking one-dimensional LiH as an example, we discuss the validity of restricting the active space to suppress the computational cost of the GFCCSD method. We show that the calculated results without bands that do not contribute to the chemical bonds are in good agreement with full-band calculations. With the GFCCSD method, we can calculate the total energies and spectral functions for periodic systems in an explicitly correlated manner.

DOI
10.1063/1.5029537

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We demonstrate that the coupled-cluster singles-and-doubles Green's function (GFCCSD) method is a powerful and prominent tool drawing the electronic band structures and the total energies, which many theoretical techniques struggle to reproduce. We have calculated single-electron energy spectra via the GFCCSD method for various kinds of systems, ranging from ionic to covalent and van der Waals, for the first time: the one-dimensional LiH chain, one-dimensional C chain, and one-dimensional Be chain. We have found that the bandgap becomes narrower than in HF due to the correlation effect. We also show that the band structures obtained from the GFCCSD method include both quasiparticle and satellite peaks successfully. Besides, taking one-dimensional LiH as an example, we discuss the validity of restricting the active space to suppress the computational cost of the GFCCSD method. We show that the calculated results without bands that do not contribute to the chemical bonds are in good agreement with full-band calculations. With the GFCCSD method, we can calculate the total energies and spectral functions for periodic systems in an explicitly correlated manner.
We present an efficient implementation of the coupled-cluster Green’s function (CCGF) method for simulating photoemission spectra of periodic systems. We formulate the periodic CCGF approach with Brillouin zone sampling in the Gaussian basis at the coupled-cluster singles and doubles (CCSD) level. To enable CCGF calculations of realistic solids, we propose an active-space self-energy correction scheme by combining CCGF with the cheaper many-body perturbation theory ( GW ) and implement the model order reduction (MOR) frequency interpolation technique. We find that the active-space self-energy correction and MOR techniques significantly reduce the computational cost of CCGF while maintaining the high accuracy. We apply the developed CCGF approaches to compute spectral properties and band structure of silicon (Si) and zinc oxide (ZnO) crystals using triple-ζ Gaussian basis sets and medium-size k -point sampling and find good agreement with experimental measurements.
We propose two schemes for interpolation of the one-particle Green's function (GF) calculated within a coupled-cluster singles and doubles (CCSD) method for a periodic system. These schemes use Wannier orbitals for circumventing huge cost for a large number of sampled k points. One of the schemes is the direct interpolation, which obtains the GF straightforwardly by using Fourier transformation. The other is the self-energy-mediated interpolation, which obtains the GF via the Dyson equation. We apply the schemes to a LiH chain and trans-polyacetylene and examine their validity in detail. It is demonstrated that the direct-interpolated GFs suffer from numerical artifacts stemming from slow convergence of CCSD GFs in real space, while the self-energy-mediated interpolation provides more physically appropriate GFs due to the localized nature of CCSD self-energies. Our schemes are also applicable to other correlated methods capable of providing GFs.
Abstract We use the cumulant Green’s functions method (CGFM) to study the single-band Hubbard model. The starting point of the method is to diagonalize a cluster (‘seed’) containing N correlated sites and employ the cumulants calculated from the cluster solution to obtain the full Green’s functions for the lattice. All calculations are done directly; no variational or self-consistent process is needed. We benchmark the one-dimensional results for the gap, the double occupancy, and the ground-state energy as functions of the electronic correlation at half-filling and the occupation numbers as functions of the chemical potential obtained from the CGFM against the corresponding results of the thermodynamic Bethe ansatz and the quantum transfer matrix methods. The particle-hole symmetry of the density of states is fulfilled, and the gap, occupation numbers, and ground-state energy tend systematically to the known results as the cluster size increases. We include a straightforward application of the CGFM to simulate the singles occupation of an optical lattice experiment with lithium-6 atoms in an eight-site Fermi-Hubbard chain near half-filling. The method can be applied to any parameter space for one, two, or three-dimensional Hubbard Hamiltonians and extended to other strongly correlated models, like the Anderson Hamiltonian, the t − J, Kondo, and Coqblin-Schrieffer models.
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 the 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 one-dimensional (1D) Hubbard model projected onto a single-site impurity problem and a half-filled two-dimensional (2D) Hubbard model projected onto a four-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 Green's function CCSD solver within the Self-Energy Embedding Theory (SEET) with Hartree-Fock (HF) and Green's Function second order (GF2) for the treatment of the environment.
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. Handling 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.
We demonstrate that the effective Hamiltonians obtained with the downfolding procedure based on double unitary coupled cluster (DUCC) ansatz can be used in the context of Green's function coupled cluster (GFCC) formalism to calculate spectral functions of molecular systems. This combined approach (DUCC-GFCC) provides a significant reduction of numerical effort and good agreement with the corresponding all-orbital GFCC methods in energy windows that are consistent with the choice of active space. These features are demonstrated on the example of four benchmark systems: H2O, N2, CO, and trans-1,3-butadiene, where DUCC-GFCC calculations were performed for active spaces of various sizes.