Cellular dynamical mean-field theory for the one-dimensional extended Hubbard model

Bolech, C. J.; Kancharla, S. S.; Kotliar, Gabriel

doi:10.1103/physrevb.67.075110

Cited by 67 publications

(96 citation statements)

References 33 publications

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“…We now discuss the one-dimensional Hubbard model, for which exact results are available from the Bethe ansatz 22 and which has been studied with CDMFT using Lanczos [11][12][13] and quantum Monte Carlo, 23 as well as with the variational cluster approximation. 24 Here going from single-site DMFT to a cluster description makes a qualitative difference; for a paramagnetic single-site calculation antiferromagnetism is completely suppressed, while on a cluster we will have short-ranged antiferromagnetic correlations, even if we impose a paramagnetic bath.…”

Section: Hubbard Chainmentioning

confidence: 99%

“…In such a situation details of the fitting procedure are important and are accordingly discussed in the literature. [11][12][13][28][29][30] To fit the Anderson parameters V l and l we use the distance function…”

Section: B Fitting the Bath Green Matrixmentioning

confidence: 99%

“…In addition we derive exact sum rules for the bath Green's functions. As an application, we investigate the one-dimensional Hubbard model with CDMFT in detail, [11][12][13] paying particular attention to the convergence with the size of both bath and cluster.…”

Section: Introductionmentioning

confidence: 99%

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Sum rules and bath parametrization for quantum cluster theories

2008

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We analyze cellular dynamical mean-field theory ͑CDMFT͒ and the dynamical cluster approximation ͑DCA͒. We derive exact sum-rules for the hybridization functions and give examples for dynamical mean-field theory, CDMFT, and DCA. For impurity solvers based on a Hamiltonian, these sum rules can be used to monitor convergence of the bath-parametrization. We further discuss how the symmetry of the cluster naturally leads to a decomposition of the bath Green matrix into irreducible components, which can be parametrized independently, and give an explicit recipe for finding the optimal bath parametrization. As a benchmark we revisit the one-dimensional Hubbard model. We carefully analyze the evolution of the density as a function of chemical potential and find that, close to the Mott transition, convergence with cluster size is unexpectedly slow. Going from one to two dimensions we find that fitting the bath becomes in general significantly more difficult, requiring a large number of bath sites. For such large baths our symmetry-adapted approach should prove crucial for finding a reliable bath-parametrization.

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Section: Hubbard Chainmentioning

confidence: 99%

Section: B Fitting the Bath Green Matrixmentioning

confidence: 99%

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Sum rules and bath parametrization for quantum cluster theories

2008

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“…The CDMFT has aleady passed several tests against the exact results and the density matrix renormalization group method in one dimension 19 , where the CDMFT scheme is expected to be worst. We employ exact diagonalization (ED) as an impurity solver of CDMFT 20 .…”

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confidence: 99%

Pseudogap and Mott transition studied by cellular dynamical mean-field theory

2007

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We study metal-insulator transitions between Mott insulators and metals. The transition mechanism completely different from the original dynamical mean field theory (DMFT) emerges from a cluster extension of it. A consistent picture suggests that the quasiparticle weight Z remains nonzero through metals and suddenly jumps to zero at the transition, while the gap opens continuously in the insulators. This is in contrast with the original DMFT, where Z continuously vanishes but the gap opens discontinuously. The present results arising from electron differentiation in momentum space agree with recent puzzling bulk-sensitive experiments on CaVO3 and SrVO3.PACS numbers: PACS: 71.30.+h; 71.10.Fd; 71.10.Pm Mechanisms and nature of correlation-induced metalinsulator transitions (MIT) are fundamental challenges in condensed matter physics 1 . Although the metals and insulators far away from the MIT are relatively well understood, electronic states dominated and controlled by the proximity of the MIT are far from complete understanding. We find many challenging phenomena such as the high-T c superconductivity in this region, which waits for better understanding of underlying proximity of MIT.The dynamical mean-field theory (DMFT) offers a clear picture of the MIT by taking the limit of high dimensions 2 . In the DMFT, the MIT is approached from metals by the reduction of the quasiparticle weight Z at the Fermi level and the transition is driven by vanishing Z 3 . At the transition, a nonzero insulating gap is already open in the density of states (DOS) as a result of the vanishing Z of the coherent peak isolated from the well-separated upper and lower Hubbard bands. Early photoemission spectroscopy (PES) and inverse-PES of Ca 1−x Sr x VO 3 4 showed a three peak structure, called a sharp coherent band at E F and the incoherent ones corresponding to the upper and lower Hubbard bands at a few electron volts above and below E F , which is consistent with the above DMFT scenario. However, recent more bulk-sensitive PES have revealed a qualitatively different and puzzling feature with a new broad peak at around 0.2eV connected to the lower Hubbard band around 1.6eV and a pseudogap formation around the Fermi level 5 . This is in marked contrast with the DMFT results.In this paper, we show that a scenario of the MIT completely different from the original DMFT emerges in two and three dimensional systems by extending the DMFT to allow the momentum dependence of the self-energy. The MIT is now not driven by a continuous reduction of Z to zero, but by the quasiparticle poles moving away from the Fermi surface, leading to a discontinuous jump of Z to zero at the Fermi level. Such a MIT is the consequence of an anisotropic extinction of the Fermi surface with the topological change, namely the electron differentiation in momentum space. We show the results by considering a cluster extension of the DMFT up to four sites for the Hubbard model on the square and cubic lattices. Our results indicate an opening of pseudogap in the DOS a...

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“…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%

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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Cellular dynamical mean-field theory for the one-dimensional extended Hubbard model

Cited by 67 publications

References 33 publications

Sum rules and bath parametrization for quantum cluster theories

Sum rules and bath parametrization for quantum cluster theories

Pseudogap and Mott transition studied by cellular dynamical mean-field theory

Extended variational cluster approximation for correlated systems

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