Finite temperature quantum embedding theories for correlated systems

Zgid, Dominika; Gull, Emanuel

doi:10.1088/1367-2630/aa5d34

Cited by 97 publications

(95 citation statements)

References 83 publications

(150 reference statements)

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“…In this section, we explore a possibility of using the CCSD self-energy in a Green's function based embedding framework, namely the self energy embedding theory (SEET) 31,50 . Originally, SEET was created to de-scribe strongly correlated molecular problems.…”

Section: Self Energy Embedding Theory With Ccsd As a Solvermentioning

confidence: 99%

“…In Sec. VI D, we describe in detail how to employ the CC Green's function as a solver for the self-energy embedding theory (SEET) [28][29][30][31][32][33][34][35][36] and we test it on an ammonia cluster employing both HF and GF2 [37][38][39][40][41][42][43][44][45] for the treatment of the environment. In the SEET framework, we analyze electronic energies, self-energies, and spectra.…”

Section: Introductionmentioning

confidence: 99%

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Coupled Cluster as an Impurity Solver for Green’s Function Embedding Methods

Shee

Zgid

2019

J. Chem. Theory Comput.

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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.

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Section: Self Energy Embedding Theory With Ccsd As a Solvermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Coupled Cluster as an Impurity Solver for Green’s Function Embedding Methods

Shee

Zgid

2019

J. Chem. Theory Comput.

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“…Applications to low-energy effective model Hamiltonians include lattice Monte Carlo [5], dynamical mean-field theory [6] with its cluster [7], multi-orbital extensions [8,9], and diagrammatic extensions [10][11][12], and diagrammatic or continuous-time quantum Monte Carlo methods [13,14]. In the context of ab initio calculations of correlated materials, examples include the GW method [15][16][17][18][19][20][21][22][23], the self-consistent second order approximation (GF2) [24][25][26][27][28][29][30][31], variants of the dynamical mean field theory [8,[32][33][34][35][36], and the self-energy embedding theory [37][38][39][40][41][42][43].…”

Section: Introductionmentioning

confidence: 99%

Sparse sampling approach to efficient ab initio calculations at finite temperature

Wallerberger

Chikano

et al. 2020

Phys. Rev. B

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Efficient ab initio calculations of correlated materials at finite temperature require compact representations of the Green's functions both in imaginary time and Matsubara frequency. In this paper, we introduce a general procedure which generates sparse sampling points in time and frequency from compact orthogonal basis representations, such as Chebyshev polynomials and intermediate representation (IR) basis functions. These sampling points accurately resolve the information contained in the Green's function, and efficient transforms between different representations are formulated with minimal loss of information. As a demonstration, we apply the sparse sampling scheme to diagrammatic GW and GF2 calculations of a hydrogen chain, of noble gas atoms and of a silicon crystal.arXiv:1908.07575v1 [cond-mat.str-el]

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“…The strategy of embedding techniques consists in solving only a small part of the system (referred to as the fragment) by a high-level method, while a low-level approximation is used for the rest of the system (referred to as the environment). Green-function-based methods have been developed, such as the widely used dynamical mean-field theory (DMFT) [7][8][9][10][11][12][13] or the more recent self-energy embedding theory (SEET) [14][15][16][17][18][19][20] . If one is interested about ground-state properties only, the Green function can be replaced by frequency-independent variables, such as the one-particle reduced density matrix (1RDM) or the electron density.…”

Section: Introductionmentioning

confidence: 99%

Projected site-occupation embedding theory

Senjean

2019

Phys. Rev. B

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Site-occupation embedding theory (SOET) [B. Senjean et al., Phys. Rev. B 97, 235105 (2018)] is an in-principle exact embedding method combining wavefunction theory and density functional theory that gave promising results when applied to the one-dimensional Hubbard model. Despite its overall good performance, SOET faces a computational cost problem as its auxiliary impurityinteracting system remains the size of the full system (which is problematic as the computational cost increases exponentially with system size). In this work, this issue is circumvented by employing the Schmidt decomposition, thus leading to a drastic reduction of the computational cost while retaining the same accuracy. We show that this projected version of SOET (P-SOET) is competitive with other embedding techniques such as density matrix embedding theory (DMET) [G. Knizia and G. K-L. Chan, Phys. Rev. Lett. 109, 186404 (2012)]. In contrast to the latter, density functional contributions come naturally into play in P-SOET's framework without any additional computational cost or double counting effect. As an important result, the density-driven Mott-Hubbard transition in one dimension (which is displayed by multiple impurity sites in DMET or in dynamical mean-field theory) is well described, for the first time, with a single impurity site. arXiv:1902.05747v3 [cond-mat.str-el]

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Finite temperature quantum embedding theories for correlated systems

Cited by 97 publications

References 83 publications

Coupled Cluster as an Impurity Solver for Green’s Function Embedding Methods

Coupled Cluster as an Impurity Solver for Green’s Function Embedding Methods

Sparse sampling approach to efficient ab initio calculations at finite temperature

Projected site-occupation embedding theory

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