Sum rules and bath parametrization for quantum cluster theories

Koch, Erik; Sangiovanni, Giorgio; Gunnarsson, O.

doi:10.1103/physrevb.78.115102

Cited by 104 publications

(110 citation statements)

References 44 publications

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“…In low-dimensional systems (single site) DMFT is in general not a good approximation. In particular, for the one-dimensional Hubbard model non-local correlations are in fact dominant 14 , leading to a complete breakdown of Fermi liquid physics and the formation of a novel low-energy fixed point, the Luttinger liquid 4 . Similarly, in two dimensions a strong influence of spin-fluctuations in the Hubbard model is expected, in particular at and close to half filling.…”

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Spectral properties of the three-dimensional Hubbard model

et al. 2011

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We present momentum resolved single-particle spectra for the three-dimensional Hubbard model for the paramagnetic and antiferromagnetically ordered phase obtained within the dynamical cluster approximation. The effective cluster problem is solved by continuous-time Quantum Monte Carlo simulations. The absence of a time discretization error and the ability to perform Monte Carlo measurements directly in Matsubara frequencies enable us to analytically continue the self-energies by maximum entropy, which is essential to obtain momentum resolved spectral functions for the Néel state. We investigate the dependence on temperature and interaction strength and the effect of magnetic frustration introduced by a next-nearest neighbor hopping. One particular question we address here is the influence of the frustrating interaction on the metal insulator transition of the three-dimensional Hubbard model.

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Spectral properties of the three-dimensional Hubbard model

et al. 2011

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“…In the case of an isotropic triangular lattice, Green's function and self-energy can be diagonalized by an analogous transformation to molecular orbitals appropriate for a three-site cluster. 45 The question then arises whether these cluster molecular orbitals in the single-band case obey a similar scenario as the multiorbital systems mentioned above.…”

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Multisite versus multiorbital Coulomb correlations studied within finite-temperature exact diagonalization dynamical mean-field theory

2008

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The influence of short-range Coulomb correlations on the Mott transition in the single-band Hubbard model at half filling is studied within cellular dynamical mean-field theory for square and triangular lattices. Finitetemperature exact diagonalization is used to investigate correlations within two-, three-, and four-site clusters. Transforming the nonlocal self-energy from a site basis to a molecular-orbital basis, we focus on the interorbital charge transfer between these cluster molecular orbitals in the vicinity of the Mott transition. In all cases studied, the charge transfer is found to be small, indicating weak Coulomb-induced orbital polarization despite sizable level splitting between orbitals. These results demonstrate that all cluster molecular orbitals take part in the Mott transition and that the insulating gap opens simultaneously across the entire Fermi surface. Thus, at half filling we do not find orbital-selective Mott transitions or a combination of band filling and Mott transition in different orbitals. Nevertheless, the approach toward the transition differs greatly between cluster orbitals, giving rise to a pronounced momentum variation along the Fermi surface, in agreement with previous works. The near absence of Coulomb-induced orbital polarization in these clusters differs qualitatively from single-site multiorbital studies of several transition-metal oxides, where the Mott phase exhibits nearly complete orbital polarization as a result of a correlation driven enhancement of the crystal-field splitting. The strong singleparticle coupling among cluster orbitals in the single-band case is identified as the source of this difference.

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“…The pioneering work of Huscroft et al [22] showed the existence of a normal-state pseudogap in the dynamical mean field approximation and many authors (using mainly N = 4 approximations) have studied its properties [23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41] and several groups (still within the 4-site approximation) have studied the interplay of superconductivity and the pseudogap [31,[42][43][44][45][46]. A key finding of the 4-site work, in contrast to the larger-cluster studies of Ref.…”

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Superconductivity and the Pseudogap in the Two-Dimensional Hubbard Model

2013

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Recently developed numerical methods have enabled the explicit construction of the superconducting state of the Hubbard model of strongly correlated electrons in parameter regimes where the model also exhibits a pseudogap and a Mott insulating phase. d x 2 −y 2 symmetry superconductivity is found to occur in proximity to the Mott insulator, but separated from it by a pseudogapped nonsuperconducting phase. The superconducting transition temperature and order parameter amplitude are found to be maximal at the onset of the normal-state pseudogap. The emergence of superconductivity from the normal state pseudogap leads to a decrease in the excitation gap. All of these features are consistent with the observed behavior of the copper-oxide superconductors. where ε p = −2t(cos p x + cos p y ) + 4t ′ cos p x cos p y an electron dispersion and U > 0 a local interaction which disfavors double occupancy of a site.In the years since Anderson's paper, the interplay of the pseudogap and superconductivity and the relation of both to the Hubbard model have been of central interest to condensed matter physicists. The existence of dwave superconductivity in the Hubbard model has been demonstrated by perturbative analytic calculations [4] (later improved by renormalization group methods [5, 6]) and by numerics [7, 8]. The issue of the pseudogap has been more controversial. It has been variously argued that the pseudogap is a signature of unusual superconducting fluctuations [9][10][11], of a competing nonsuperconducting phase or regime [3, 12], or of physics not contained in the Hubbard model [13]. Theoretical determination of the interplay of the pseudogap and superconductivity in the Hubbard model is important in helping resolve this controversy, and will provide insight into the pseudogap phenomenon and into strongly correlated superconductivity more generally, but this requires access to intermediate or strong couplings for which perturbation theory is inadequate. The development of cluster dynamical mean field theory [15] has provided important nonperturbative information about the Hubbard model. Dynamical mean field theory approximates the electron self-energy in terms of a finite number of auxiliary functions determined from the solution of an N -site quantum impurity model and becomes exact as N tends to infinity. In this Letter we use dynamical mean field methods to determine the interplay of superconductivity and the pseudogap in the Hubbard model. This is challenging because the theory

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Sum rules and bath parametrization for quantum cluster theories

Cited by 104 publications

References 44 publications

Spectral properties of the three-dimensional Hubbard model

Spectral properties of the three-dimensional Hubbard model

Multisite versus multiorbital Coulomb correlations studied within finite-temperature exact diagonalization dynamical mean-field theory

Superconductivity and the Pseudogap in the Two-Dimensional Hubbard Model

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