Five Years of Density Matrix Embedding Theory

Wouters, Sebastian; Jiménez-Hoyos, Carlos A.; Chan, Garnet Kin‐Lic

doi:10.1002/9781119129271.ch8

Cited by 30 publications

(46 citation statements)

References 24 publications

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“…4. For each cluster κ, solve the ground-state equation (24) with ED and the response equations (25,26). From the ground and response states, construct the impurity Green's function (27) and the new impurity self-energy via the Dyson equation (28).…”

Section: Construct Static and Dynamic Bath Orbitals According Tomentioning

confidence: 99%

“…The ω-DMFT approach detailed in this work can be considered an extension of the EwDMET method for spectral embedding, allowing for full dynamical effects of the impurity, and building on and generalizing the previous work of the construction of (non-self-consistent) bath spaces for spectral DMET 23,26 . The systematic expansion in static bath orbitals of EwDMET is generalized for a systematic expansion of explicitly dynamic bath orbitals to converge the bath discretization error for fully dynamical properties.…”

Section: Introductionmentioning

confidence: 99%

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Frequency-dependent and algebraic bath states for a dynamical mean-field theory with compact support

Nusspickel

Booth

2020

Phys. Rev. B

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We demonstrate an algebraic construction of frequency-dependent bath orbitals which can be used in a robust and rigorously self-consistent DMFT-like embedding method, here called ω-DMFT, suitable for use with Hamiltonian-based impurity solvers. These bath orbitals are designed to exactly reproduce the hybridization of the impurity to its environment, while allowing for a systematic expansion of this bath space as impurity interactions couple frequency points. In this way, the difficult non-linear fit of bath parameters necessary for many Hamiltonian-formulation impurity solvers in DMFT is avoided, while the introduction of frequency dependence in this bath space is shown to allow for more compact bath sizes. This has significant potential use with a number of new, emerging Hamiltonian solvers which allow for the embedding of large impurity spaces within a DMFT framework. We present results of the ω-DMFT approach for the Hubbard model on the Bethe lattice, a 1D chain, and the 2D square lattice, which show excellent agreement with standard DMFT results, with fewer bath orbitals and more compact support for the hybridization representation in the key impurity model of the method. arXiv:1909.07713v1 [cond-mat.str-el]

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Section: Construct Static and Dynamic Bath Orbitals According Tomentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Frequency-dependent and algebraic bath states for a dynamical mean-field theory with compact support

Nusspickel

Booth

2020

Phys. Rev. B

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“…For the calculation of non-dynamical properties, density matrix embedding theory (DMET) [27][28][29][30][31][32][33][34][35][36], or the related rotationally invariant slave bosons technique [37,38], has become a viable alternative to DMFT. In standard DMET, the embedding procedure relies on the Schmidt decomposition of a mean-field many-body wavefunction.…”

Section: Introductionmentioning

confidence: 99%

Site-occupation Green's function embedding theory: A density functional approach to dynamical impurity solvers

2019

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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 with the self-energy of the two-level Anderson model is constructed and successfully applied to the one-dimensional Hubbard model. Unlike in previous implementations of SOET, no many-body wavefunction is needed, thus reducing drastically the computational cost of the method.

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“…The self-consistency for DMET is based on the density matrix, instead of the frequency-dependent Green's function in DMFT. Information about excited states in DMET can still be explored [33,34].…”

Section: Introductionmentioning

confidence: 99%

“…[31,32] and is illustrated extensively in Ref. [34]. Other methods are also possible: single-particle states from Hartree-Fock-Bogoliubov theory [35,36] and antisymmetrized geminal power (AGP) wave functions [37] have also been used.…”

Section: Introductionmentioning

confidence: 99%

Block product density matrix embedding theory for strongly correlated spin systems

et al. 2017

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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.

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Five Years of Density Matrix Embedding Theory

Cited by 30 publications

References 24 publications

Frequency-dependent and algebraic bath states for a dynamical mean-field theory with compact support

Frequency-dependent and algebraic bath states for a dynamical mean-field theory with compact support

Site-occupation Green's function embedding theory: A density functional approach to dynamical impurity solvers

Block product density matrix embedding theory for strongly correlated spin systems

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