Dynamical Mean-Field Theory

Vollhardt, D.; Byczuk, Krzysztof; Kollar, Marcus

doi:10.1007/978-3-642-21831-6_7

Cited by 18 publications

(22 citation statements)

References 174 publications

(311 reference statements)

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“…Such NFL behaviour indeed bears some superficial resemblance to that found in a certain class of the heavy-fermion compounds [45] and DMFT calculations [46]. However, it is also plagued with such spurious features as potentially multiple Fermi surfaces, dispersionless peaks, and log-oscillating ω-dependence [35][36][37][38][39][40][41][42][43][44].…”

Section: Condensed Matter Holography: the Evidencesupporting

confidence: 52%

Demystifying the holographic mystique: A critical review

Khveshchenko¹

2016

Lith. J. Phys.

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Thus far, in spite of many interesting developments, the overall progress towards a systematic study and classification of various 'strange' metallic states of matter has been rather limited. To that end, it was argued that a recent proliferation of the ideas of holographic correspondence originating from string theory might offer a possible way out of the stalemate. However, after almost a decade of intensive studies into the proposed extensions of the holographic conjecture to a variety of condensed matter problems, the validity of this intriguing approach remains largely unknown. This discussion aims at ascertaining its true status and elucidating the conditions under which some of its predictions may indeed be right (albeit, possibly, for a wrong reason).Keywords: strongly correlated systems, holographic correspondence, transport theory, strange metals, analogue gravity PACS: 71.27.+a Condensed matter holography: the promiseAmong the outstanding grand problems in condensed matter physics is that of a deeper understanding and classification of the so-called 'strange metals' or compressible non-Fermi liquid (NFL) states of the strongly interacting systems. However, despite all the effort and a plethora of the important and nontrivial results obtained with the use of the traditional techniques, this program still remains far from completion.As an alternate approach, over the past decade there have been numerous attempts inspired by the hypothetical idea of holographic correspondence which originated from string/gravity/high energy theory (where it is known under the acronym AdS/ CFT) to adapt its main concepts to various condensed matter (or, even more generally, quantum manybody) systems at finite densities and temperatures [1][2][3][4][5][6][7].In its original context, the bona fide holographic principle postulates that certain d + 1-dimensional ('boundary') quantum field theories (e. g. the maximally supersymmetric SU(N) gauge theory) may allow for a dual description in terms of a string theory which, upon a proper compactification, amounts to a certain d + 2-dimensional ('bulk') supergravity. Moreover, in the strong coupling limit (characterized in terms of the t'Hooft coupling constant λ = g 2 N >> 1) and for a large rank N > > 1 of the gauge symmetry group, the bulk description can be further reduced down to a weakly fluctuating gravity model which can even be treated semiclassically at the lowest (0th) order of the underlying 1/N-expansion.In the practical applications of the holographic conjecture, the partition function of a strongly interacting boundary theory with the Lagrangian L(ϕ a ) would then be approximated by a saddle-point (classical) value of the bulk action described by the Lagrangian L(g μν ,…) which includes gravity and other fields dual to their boundary counterparts [1][2][3][4][5][6][7][8] (1) evaluated with the use of a fixed background metric ,while any quantum corrections would usually be neglected by invoking the small parameter 1/N.

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Section: Condensed Matter Holography: the Evidencesupporting

confidence: 52%

Demystifying the holographic mystique: A critical review

Khveshchenko¹

2016

Lith. J. Phys.

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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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“…Σ ij (ω) = Σ i (ω)δ ij [16,17,18,19,20]. Solving the full R-DMFT self-consistent equations is computationally exhaustive.…”

Section: Model and Formalismmentioning

confidence: 99%

Screening of a single impurity and Friedel oscillations in Fermi liquids

Chatterjee

Byczuk

2015

J. Phys.: Conf. Ser.

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Abstract.We numerically study Friedel Oscillations and screening eect around a single impurity in one-and two-dimensional interacting lattice electrons. The interaction between electrons is accounted for by using a momentum independent self-energy obeying the Luttinger theorem. It is observed in one-dimensional systems that the amplitude of oscillations is systematically damped with increasing the interaction while the period remains unchanged. The variation of screening charge with the impurity potential is discussed. We see that the screening charge is suppressed by the interactions. In case of two-dimensional systems the surface oscillations around the impurity are more localized with increasing the interactions.

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Dynamical Mean-Field Theory

Cited by 18 publications

References 174 publications

Demystifying the holographic mystique: A critical review

Demystifying the holographic mystique: A critical review

Projected site-occupation embedding theory

Screening of a single impurity and Friedel oscillations in Fermi liquids

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