Cluster methods for strongly correlated electron systems

Biroli, Giulio; Kotliar, Gabriel

doi:10.1103/physrevb.65.155112

Cited by 96 publications

(104 citation statements)

References 12 publications

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“…Different schemes of estimators have been discussed in Ref. 13. When the solutions are confined to be spatial translation invariant, each cluster becomes identical.…”

Section: B Evca For Density-density Interactionmentioning

confidence: 99%

“…Recently, detailed comparisons between the performance of DCA and CDMFT have been made. 13,43 It was pointed out that the real-space formula of DCA can be obtained by replacing the bare electron dispersion ǫ(k) in the CDMFT equations with a different one ǫ cyc (K, K c ). This means that the formula of CDMFT can be changed into that of DCA by simply replacing the bare G −1 0CDMF T in that theory with the corresponding G −1 0DCA , and vice versa.…”

Section: Translation-invariant Vca and Evcamentioning

confidence: 99%

“…G is defined as in Eq. (13). We define the density-density Green's function, phonon Green's function, and phonon self-energy as…”

Section: B the Role Of Hubbard-stratonovich Transformationmentioning

confidence: 99%

“…Its results are found to be quantitatively close to the EDMFT results. Finally, based on the real space formula of the DCA by Biroli et al, 13 we propose a VCA and EVCA that utilize clusters with periodic boundary conditions. In the continuous limit, this version of the VCA will lead to the DCA instead of the CDMFT, and correspondingly, the EVCA formula will lead to the extended version of DCA.…”

Section: Introductionmentioning

confidence: 99%

“…In order to take into account the spatial fluctuations beyond DMFT, besides the systematic 1/D expansion approach, 10,11 various cluster algorithms, e.g., the cellular DMFT (CDMFT), 12,13,14,15 and the dynamical cluster approximation (DCA), 16 have been proposed. The former uses clusters with open boundary conditions, and the latter has periodic boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

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Extended variational cluster approximation for correlated systems

Tong

2005

Phys. Rev. B

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The variational cluster approximation (VCA) proposed by M. Potthoff et al. [Phys. Rev. Lett. 91, 206402 (2003)] is extended to electron or spin systems with nonlocal interactions. By introducing more than one source field in the action and employing the Legendre transformation, we derive a generalized self-energy functional with stationary properties. Applying this functional to a proper reference system, we construct the extended VCA (EVCA). In the limit of continuous degrees of freedom for the reference system, EVCA can recover the cluster extension of the extended dynamical mean-field theory (EDMFT). For a system with correlated hopping, the EVCA recovers the cluster extension of the dynamical mean-field theory for correlated hopping. Using a discrete reference system composed of decoupled three-site single impurities, we test the theory for the extended Hubbard model. Quantitatively good results as compared with EDMFT are obtained. We also propose VCA (EVCA) based on clusters with periodic boundary conditions. It has the (extended) dynamical cluster approximation as the continuous limit. A number of related issues are discussed.

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“…Different schemes of estimators have been discussed in Ref. 13. When the solutions are confined to be spatial translation invariant, each cluster becomes identical.…”

Section: B Evca For Density-density Interactionmentioning

confidence: 99%

Section: Translation-invariant Vca and Evcamentioning

confidence: 99%

“…G is defined as in Eq. (13). We define the density-density Green's function, phonon Green's function, and phonon self-energy as…”

Section: B the Role Of Hubbard-stratonovich Transformationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Extended variational cluster approximation for correlated systems

Tong

2005

Phys. Rev. B

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Realistic investigations of correlated electron systems with LDA + DMFT

Held¹,

Некрасов

Keller

et al. 2006

Physica Status Solidi (b)

242

263

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PACS 71.15.Mb, 71.27.+ a, 71.30.+ h Conventional band structure calculations in the local density approximation (LDA) [1 -3] are highly successful for many materials, but miss important aspects of the physics and energetics of strongly correlated electron systems, such as transition metal oxides and f-electron systems displaying, e.g., Mott insulating and heavy quasiparticle behavior. In this respect, the LDA + DMFT approach which merges LDA with a modern many-body approach, the dynamical mean-field theory (DMFT), has proved to be a breakthrough for the realistic modeling of correlated materials. Depending on the strength of the electronic correlation, a LDA + DMFT calculation yields the weakly correlated LDA results, a strongly correlated metal, or a Mott insulator. In this paper, the basic ideas and the set-up of the LDA + DMFT(X) approach, where X is the method used to solve the DMFT equations, are discussed. Results obtained with X = QMC (quantum Monte Carlo) and X = NCA (non-crossing approximation) are presented and compared, showing that the method X matters quantitatively. We also discuss LDA + DMFT results for two prime examples of correlated materials, i.e., V 2 O 3 and Ce which undergo a Mott -Hubbard metal -insulator and volume collapse transition, respectively.

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Non-perturbative treatment of the attractive Hubbard model

Koinov¹

2009

phys. stat. sol. (b)

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We have used a Hubbard-Stratonovich transformation to convert the quartic Hubbard problem of interacting electrons into more tractable quadratic problem of non-interacting electrons coupled to a Bose field. The Dyson and the BetheSalpeter (BS) equations for the corresponding Green functions are derived by applying a functional derivative technique combined with the method of Legendre transform. This approach allows us to obtain exact relations between singleand two-particle quantities. We have compared the selfconsistent relationship between mass operator and two-particle Green function with the similar relationship in the two-particle self-consistent (TPSC) approximation, and came up with the conclusion that the accuracy of the TPSC approximation is questionable because: (i) if equal-time pair-correlation function is set to one, the mass operator in TPSC approximation differs significantly from the exact mass operator; and (ii) the TPSC approximation does not take into account the Hartree part of the mass operator. The latter results in missing exchange interaction in the BS equation. A generalized random-phase approximation is applied to demonstrate the important role of the exchange interaction when BS equation is used to study collective excitation spectrum of the attractive Hubbard model. 1 Introduction The discovery of the high-T c superconductors has revived interest in strongly correlated electron systems. The single-band Hubbard model, with on-site interaction U 0 and nearest-neighbor hopping t, is the simplest model of correlated electrons. It has been extensively studied, for example, in the context of hightemperature superconductors. Despite the apparent simplicity of the Hubbard model, it is difficult to describe the intermediate region where neither the potential nor the kinetic energy dominate, because in this region we have to deal with a drastic renormalization of the single-particle spectrum without the presence of any small many-body parameters. The latter requires non-perturbative many-body treatment of the problem.The attractive Hubbard model is described by the following Hamiltonian:

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Cluster methods for strongly correlated electron systems

Cited by 96 publications

References 12 publications

Extended variational cluster approximation for correlated systems

Extended variational cluster approximation for correlated systems

Realistic investigations of correlated electron systems with LDA + DMFT

Non-perturbative treatment of the attractive Hubbard model

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