Variational Cluster Approach to Correlated Electron Systems in Low Dimensions

Potthoff, Michael; Aichhorn, Markus; Dahnken, Christopher

doi:10.1103/physrevlett.91.206402

Cited by 341 publications

(456 citation statements)

References 21 publications

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“…In order to take electron correlation effects into account, we treat the electronic interactions in (1) within the VCA, 47,48 which is a quantum cluster method based on the self-energy functional theory 49 . The VCA first introduces disconnected clusters of finite size, for which the cluster self-energy Σ can be computed exactly.…”

Section: Variational Cluster Approximationmentioning

confidence: 99%

Competition between excitonic charge and spin density waves: Influence of electron-phonon and Hund's rule couplings

et al. 2015

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We analyze the stability of excitonic ground states in the two-band Hubbard model with additional electron-phonon and Hund's rule couplings using a combination of mean-field and variational cluster approaches. We show that both the interband Coulomb interaction and the electron-phonon interaction will cooperatively stabilize a charge density wave (CDW) state which typifies an "excitonic" CDW if predominantly triggered by the effective interorbital electron-hole attraction or a "phononic" CDW if mostly caused by the coupling to the lattice degrees of freedom. By contrast, the Hund's rule coupling promotes an excitonic spin density wave. We determine the transition between excitonic charge and spin density waves and comment on a fixation of the phase of the excitonic order parameter that would prevent the formation of a superfluid condensate of excitons. The implications for exciton condensation in several material classes with strongly correlated electrons are discussed.

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Section: Variational Cluster Approximationmentioning

confidence: 99%

Competition between excitonic charge and spin density waves: Influence of electron-phonon and Hund's rule couplings

et al. 2015

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“…This particular implementation of the self-energy functional with no bath (contrary to DMFT) goes under the name of the variational cluster approximation (VCA). DMFT and generalizations thereof, (such as Cellular Dynamical Mean-Field Theory (CDMFT)) can be obtained as various special cases of SFA 7,8 corresponding to different choices of reference systems and/or approximations of the stationarity condition. (The functionals of Chitra and Kotliar 5 and of Potthoff 7,8 are in fact identical, as shown in Appendix C1).…”

Section: Introductionmentioning

confidence: 99%

Convexity of the self-energy functional in the variational cluster approximation

2008

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In the variational cluster approximation (VCA) (or variational cluster perturbation theory), widely used to study the Hubbard model, a fundamental problem that renders variational solutions difficult in practice is its known lack of convexity at stationary points, i.e. the physical solutions can be saddle points rather than extrema of the self-energy functional. Here we suggest two different approaches to construct a convex functional Ω [Σ]. In the first approach, one can show analytically that in the approximation where the irreducible particle-hole vertex depends only on center of mass coordinates, the functional is convex away from phase transitions in the corresponding channel. Numerical tests on a tractable version of that functional show that convexity can be a nuisance when looking for instabilities both in the pairing and particle-hole channels. Therefore, an alternative phenomenological functional is proposed. Convexity is explicitly enforced only with respect to a restricted set of variables, such as the cluster chemical potential that is known to be otherwise problematic. Numerical tests show that our functional is convex at the physical solutions of VCA and allows second-order phase transitions in the pairing channel as well. This opens the way to the use of more efficient algorithms to find solutions of the VCA equations.

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“…[50][51][52][53] In the SFT, the grand potential Ω of the original system is given by a functional of the self-energy. In the VCA and CDIA, we introduce disconnected finitesize clusters that are solved exactly as a reference system.…”

Section: Vca and Cdiamentioning

confidence: 99%

“…[42][43][44][45][46][47][48][49] We have so far studied the excitonic phases of the EFKM and multiband Hubbard models using the variational cluster approximation (VCA) based on the exact diagonalization of small clusters. 50,51) However, some difficulty arises in such a small-cluster approach, particularly when we calculate physical quantities as a function of the model parameters. For example, the number of electrons in the valence and conduction bands changes discontinuously as a function of energy-level splitting between the valence and conduction orbitals.…”

Section: Introductionmentioning

confidence: 99%

Excitonic Insulator State of the Extended Falicov–Kimball Model in the Cluster Dynamical Impurity Approximation

et al. 2017

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We comparatively study the excitonic insulator state in the extended Falicov-Kimball model (EFKM, a spinless two-band model) on the two-dimensional square lattice using the variational cluster approximation (VCA) and the cluster dynamical impurity approximation (CDIA). In the latter, the particle-bath sites are included in the reference cluster to take into account the particle-number fluctuations in the correlation sites. We thus calculate the particle-number distribution, order parameter, ground-state phase diagram, anomalous Green's function, and pair coherence length, thereby demonstrating the usefulness of the CDIA in the discussion of the excitonic condensation in the EFKM. IntroductionThe excitonic phases, often referred to as excitonic insulators (EIs), are the states where the valence and conduction bands are hybridized spontaneously by the interband Coulomb interaction, and have been predicted to occur near the semimetal-semiconductor phase boundary as the quantum condensation of electron-hole pairs (excitons). [1][2][3][4][5][6] In the semimetallic region, where the Coulomb interaction is largely screened by free carriers, the excitonic phase is described in analogy to the BCS theory of superconductivity, whereas in the semiconducting region, it is described as the Bose-Einstein condensation (BEC) of preformed excitons (or strongly bound electron-hole pairs). Thus, the BCS-BEC crossover is expected to occur by controlling the band gap from a negative value to a positive one. [7][8][9] In recent years, the possible realization of spinsinglet excitonic condensation has been suggested for transition-metal chalcogenides such as 1T -TiSe 2 and Ta 2 NiSe 5 . 10-23) The spin-triplet excitonic condensation has also been suggested to occur in the high-spin/lowspin crossover region of some cobalt oxide materials with the cubic perovskite structure. 24-29) Because these materials are among transition-metal chalcogenides and oxides, where the effects of electron correlations are strong, one must reconsider the excitonic phases from the standpoint of strongly correlated electron systems. 30-32) Thus, the lattice models such as Hubbard models, rather than the gas models, are appropriate for use. The spinless extended Falicov-Kimball model (EFKM) is the simplest lattice model for describing the excitonic phases, and has been used to discuss, for example, the BCS-BEC crossover of the excitonic condensation. 33-41) The multiband Hubbard model, taking into account the spin de-

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Variational Cluster Approach to Correlated Electron Systems in Low Dimensions

Cited by 341 publications

References 21 publications

Competition between excitonic charge and spin density waves: Influence of electron-phonon and Hund's rule couplings

Competition between excitonic charge and spin density waves: Influence of electron-phonon and Hund's rule couplings

Convexity of the self-energy functional in the variational cluster approximation

Excitonic Insulator State of the Extended Falicov–Kimball Model in the Cluster Dynamical Impurity Approximation

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