Dynamical mean-field theory, density-matrix embedding theory, and rotationally invariant slave bosons: A unified perspective

Ayral, Thomas; Lee, Tsung-Han; Kotliar, Gabriel

doi:10.1103/physrevb.96.235139

Cited by 50 publications

(43 citation statements)

References 56 publications

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“…Mott) physics to be described on the lattice at lower orders than constraining the central moments of the spectrum. Although a self-consistent matching of energy-weighted density matrices between the lattice and cluster model will allow for dynamical correlated effects to be returned from the cluster to the lattice, a local static 'correlation' potential as optimized within DMET (v c ) is insufficient to rigorously match even the RDM (0th hole moment), and this becomes increasingly true for higher moments 19,20 . To overcome this, we supplement v c with a set of n aux auxiliary single-particle degrees of freedom, which couple to the impurity space on the physical lattice, and to all symmetry-equivalent n cells impurity cells.…”

Section: Methodsmentioning

confidence: 99%

Rigorous wave function embedding with dynamical fluctuations

Fertitta

Booth

2018

Phys. Rev. B

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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 correlated dynamics of the paradigmatic Bethe lattice Hubbard model, as well as detailing cluster extensions in the one-dimensional Hubbard chain where we clearly show the benefits of this rapidly convergent description of correlated environmental fluctuations. arXiv:1808.09321v4 [cond-mat.str-el]

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Section: Methodsmentioning

confidence: 99%

Rigorous wave function embedding with dynamical fluctuations

Fertitta

Booth

2018

Phys. Rev. B

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“…The second step follows the implementation detailed in Ref. 54 . Finally, the embedded problem is solved either analytically for a single impurity site (see Appendix A) or numerically for multiple impurities by using the Block code of density matrix renormalization group (DMRG) [59][60][61][62][63] .…”

Section: Approximate Functionalsmentioning

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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“…The rotationally invariant slave boson (RISB) form (28,29) has been shown to be quite accurate for the estimation of total energies. Recently, simple connections among all these approaches have been uncovered (30,31), with LDA+G being equivalent to LDA+RISB and DMET appearing as a limiting case of RISB. For these simplified methods to reach first-principles status, a prescription for the determination of the Hubbard U tensor to be used is needed.…”

Section: Green's Function Approachmentioning

confidence: 99%

Toward a predictive theory of correlated materials

Kent

Kotliar

2018

Science

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Correlated electron materials display a rich variety of notable properties ranging from unconventional superconductivity to metal-insulator transitions. These properties are of interest from the point of view of applications but are hard to treat theoretically, as they result from multiple competing energy scales. Although possible in more weakly correlated materials, theoretical design and spectroscopy of strongly correlated electron materials have been a difficult challenge for many years. By treating all the relevant energy scales with sufficient accuracy, complementary advances in Green's functions and quantum Monte Carlo methods open a path to first-principles computational property predictions in this class of materials.

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Dynamical mean-field theory, density-matrix embedding theory, and rotationally invariant slave bosons: A unified perspective

Cited by 50 publications

References 56 publications

Rigorous wave function embedding with dynamical fluctuations

Rigorous wave function embedding with dynamical fluctuations

Projected site-occupation embedding theory

Toward a predictive theory of correlated materials

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