The Hubbard model within the equations of motion approach

Mancini, Ferdinando; Avella, Adolfo

doi:10.1080/00018730412331303722

Cited by 102 publications

(231 citation statements)

References 454 publications

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“…Much more intriguing, and challenging, is the 2D case, most relevant for high-temperature superconductivity and the rapidly emerging field of oxide thin films and heterostructures. In fact, this issue has been intensely debated since the Seventies: On the one hand, several analytical and numerical results [15][16][17][18][19][20] suggested that a metallic phase is found at weak coupling, with a MIT at a finite U c . At the same time, calculations with the twoparticle self-consistent (TPSC) approach [21][22][23] showed a pseudogap in the perturbative regime of small U [24].…”

Section: Introductionmentioning

confidence: 99%

Fate of the false Mott-Hubbard transition in two dimensions

et al. 2015

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We have studied the impact of non-local electronic correlations at all length scales on the MottHubbard metal-insulator transition in the unfrustrated two-dimensional Hubbard model. Combining dynamical vertex approximation, lattice quantum Monte-Carlo and variational cluster approximation, we demonstrate that scattering at long-range fluctuations, i.e., Slater-like paramagnons, opens a spectral gap at weak-to-intermediate coupling -irrespectively of the preformation of localized or short-ranged magnetic moments. This is the reason, why the two-dimensional Hubbard model has a paramagnetic phase which is insulating at low enough temperatures for any (finite) interaction and no Mott-Hubbard transition is observed. Introduction.The Mott-Hubbard metal-insulator transition (MIT) [1] is one of the most fundamental hallmarks of the physics of electronic correlations. Nonetheless, astonishingly little is known exactly, even for its simplest modeling, i.e., the single-band Hubbard Hamiltonian [2]: Exact solutions for this model are available only in the extreme, limiting cases of one and infinite dimensions.In one dimension (1D), the Bethe ansatz shows that there is actually no Mott-Hubbard transition [3][4][5]; or, in other words, it occurs for a vanishingly small Hubbard interaction U : At any U > 0 the 1D-Hubbard model is insulating at half filling. One dimension is, however, rather peculiar: While there is no antiferromagnetic ordering even at temperature T = 0, antiferromagnetic spin fluctuations are strong and long-ranged, decaying slowly, i.e., algebraically. Also the (doped) metallic phase is not a standard Fermi liquid but a Luttinger liquid.For the opposite extreme, infinite dimensions, the dynamical mean field theory (DMFT) [6] becomes exact [7], which allows for a clear-cut and -to a certain extentalmost "idealized" description of a pure Mott-Hubbard MIT. In fact, since in D = ∞ only local correlations survive [7], the Mott-Hubbard insulator of DMFT consists of a collection of localized (but not long-range ordered) magnetic moments. This way, if antiferromagnetic order is neglected or sufficiently suppressed, DMFT describes a first-order MIT [6,8], ending with a critical endpoint.As an approximation, DMFT is applicable to the more realistic cases of the three-and two-dimensional Hubbard models. However, the DMFT description of the MIT is the very same here, since only the non-interacting density of states (DOS) and in particular its second moment enter. This is a natural shortcoming of the mean-field nature of DMFT: antiferromagnetic fluctuations have no effect at all on the DMFT spectral function or self-energy above the antiferromagnetic ordering temperature T N .In 3D, antiferromagnetic fluctuations reduce T N siz-

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Section: Introductionmentioning

confidence: 99%

Fate of the false Mott-Hubbard transition in two dimensions

et al. 2015

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“…where the zero-frequency function Γ(i, j) is defined as Γ explicitly appears in the expression of the correlation function when the field ψ is boson-like, that is, ψ is constituted of an even number of original electronic (i.e., fermionic) operators 1,2 . Hereafter, we focus on such a case.…”

Section: Introductionmentioning

confidence: 99%

Nonergodic dynamics of the extended anisotropic Heisenberg chain

2006

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The issue of ergodicity is often underestimated. The presence of zero-frequency excitations in bosonic Green's functions determine the appearance of zero-frequency momentum-dependent quantities in correlation functions. The implicit dependence of matrix elements make such quantities also relevant in the computation of susceptibilities. Consequently, the correct determination of these quantities is of great relevance and the well-established practice of fixing them by assuming the ergodicity of the dynamics is quite questionable as it is not justifiable a priori by no means. In this manuscript, we have investigated the ergodicity of the dynamics of the z-component of the spin in the 1D Heisenberg model with anisotropic nearest-neighbor and isotropic next-nearest-neighbor interactions. We have obtained the zero-temperature phase diagram in the thermodynamic limit by extrapolating Exact and Lanczos diagonalization results computed on chains with sizes L = 6 ÷ 26. Two distinct non-ergodic regions have been found: one for J ′ /Jz 0.3 and |J ⊥ |/Jz < 1 and another for J ′ /Jz 0.25 and |J ⊥ |/Jz = 1. On the contrary, finite-size scaling of T = 0 results, obtained by means of Exact diagonalization on chains with sizes L = 4 ÷ 18, indicates an ergodic behavior of dynamics in the whole range of parameters.

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“…For this purpose the first order corrections over W/SJ in the terminal part Λ 1 and the second order in the self-energy Σ 2 over hopping will be calculated elsewhere. Similarly to what was done by us for the Hubbard model [9] we extract from Σ 2 a static contribution with some adjustive parameters, which are determined from fundamental conditions for electron GF [10]. Preliminary analysis shows that quasiparticle subbands can be overlapped which leads to a metal-insulator phase transition.…”

Section: Limit Of Classical Spinmentioning

confidence: 99%

A generating functional approach to the sd-model with strong correlations

Izyumov¹,

Chaschin²,

Alexeev³

2005

Condens. Matter Phys.

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A Kadanoff-Baym-type generating functional approach, earlier developed by the authors to strongly correlated systems, is applied to the sd-model with strong sd-coupling. Formalism of the Hubbard X -operators was used, and equation for electron Green's function was derived with functional derivatives over external fluctuating fields. Iterations in this equation generate a perturbation theory near the atomic limit. Hartree-Fock type approximation is developed within the framework of this theory, and the problem of a metal-insulator phase transition in sd-model is discussed.

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The Hubbard model within the equations of motion approach

Cited by 102 publications

References 454 publications

Fate of the false Mott-Hubbard transition in two dimensions

Fate of the false Mott-Hubbard transition in two dimensions

Nonergodic dynamics of the extended anisotropic Heisenberg chain

A generating functional approach to the sd-model with strong correlations

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