Nonlocal correlations and spectral properties of the Falicov-Kimball model

Ribic, T.; Rohringer, G.; Held, Karsten

doi:10.1103/physrevb.93.195105

Cited by 50 publications

(68 citation statements)

References 54 publications

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“…(34)] itself diverges. These divergences in the phase-diagram occur also along several lines 27 , at first glance very similar to those of the first divergence. Their positions, however, are (for a given T ) always at larger interactions compared to the singularities of the first type.…”

Section: B Dmft Divergences In the Falicov-kimball Modelmentioning

confidence: 79%

“…A full understanding of all non-perturbative aspects [24][25][26][27][30][31][32]35,38 of the (non-relativistic) quantum many-body theory will certainly require considerable additional efforts. These efforts might be, however, highly rewarding in the perspective of gaining the total control of the theory of correlated electron systems in their most elusive, but phenomenologically interesting, parameter regions.…”

Section: Discussionmentioning

confidence: 99%

“…Moreover, but only in the FK model, a second kind of divergences appear 27 , with qualitatively different properties: these divergences, as well their eigenvector, are not localized in frequency and, hence, not associated with a unique energy scale.…”

Section: B Dmft Divergences In the Falicov-kimball Modelmentioning

confidence: 99%

“…The qualitative difference between these two kinds of divergences in the FK model is reflected in a corresponding different structure of the singular eigenvectors of the generalized susceptibility 27 . In fact, according to the discussion in Sec.…”

Section: B Dmft Divergences In the Falicov-kimball Modelmentioning

confidence: 99%

“…First specific reports about unexpected theoretical consequences induced by the breakdown of the many-body perturbation expansion have been recently presented by several groups. Such effects range from the occurrence [24][25][26][27] of low-frequency divergences of two-particle irreducible vertex functions in the Hubbard 28 and Falicov-Kimball 29 models to the multivaluedness [30][31][32][33][34][35][36] of the electronic self-energy expressed as a functional of the (interacting) Green's function or, equivalently, of the Luttinger-Ward functional. All these manifestations of non-perturbativeness are interconnected and represent different aspects of the same problem, as suggested in some of the abovementioned works.…”

Section: Introductionmentioning

confidence: 99%

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Nonperturbative landscape of the Mott-Hubbard transition: Multiple divergence lines around the critical endpoint

et al. 2016

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We analyze the highly non-perturbative regime surrounding the Mott-Hubbard metal-to-insulator transition (MIT) by means of dynamical mean field theory (DMFT) calculations at the two-particle level. By extending the results of Schäfer, et al. [Phys. Rev. Lett. 110, 246405 (2013)] we show the existence of infinitely many lines in the phase diagram of the Hubbard model where the local Bethe-Salpeter equations, and the related irreducible vertex functions, become singular in the charge as well as the particle-particle channel. By comparing our numerical data for the Hubbard model with analytical calculations for exactly solvable systems of increasing complexity [disordered binary mixture (BM), Falicov-Kimball (FK) and atomic limit (AL)], we have (i) identified two different kinds of divergence lines; (ii) classified them in terms of the frequency-structure of the associated singular eigenvectors; (iii) investigated their relation to the emergence of multiple branches in the Luttinger-Ward functional. In this way, we could distinguish the situations where the multiple divergences simply reflect the emergence of an underlying, single energy scale ν * below which perturbation theory is no longer applicable, from those where the breakdown of perturbation theory affects, not trivially, different energy regimes. Finally, we discuss the implications of our results on the theoretical understanding of the non-perturbative physics around the MIT and for future developments of many-body algorithms applicable in this regime.

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Section: B Dmft Divergences In the Falicov-kimball Modelmentioning

confidence: 79%

Section: Discussionmentioning

confidence: 99%

Section: B Dmft Divergences In the Falicov-kimball Modelmentioning

confidence: 99%

Section: B Dmft Divergences In the Falicov-kimball Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Nonperturbative landscape of the Mott-Hubbard transition: Multiple divergence lines around the critical endpoint

et al. 2016

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Second-order dual fermion for multi-orbital systems

Loon

2021

J. Phys.: Condens. Matter

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In dynamical mean-field theory, the correlations between electrons are assumed to be purely local. The dual fermion approach provides a systematic way of adding non-local corrections to the dynamical mean-field theory starting point. Initial applications of this method were largely restricted to the single-orbital Hubbard model. Here, we present an implementation of second-order dual fermion for general multi-orbital systems and use this approach to investigate spatial correlations in SrVO3. In addition, the approach is benchmarked in several exactly solvable small systems.

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How to read between the lines of electronic spectra: the diagnostics of fluctuations in strongly correlated electron systems

Schäfer

Toschi

2021

J. Phys.: Condens. Matter

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While calculations and measurements of single-particle spectral properties often offer the most direct route to study correlated electron systems, the underlying physics may remain quite elusive, if information at higher particle levels is not explicitly included. Here, we present a comprehensive overview of the different approaches which have been recently developed and applied to identify the dominant two-particle scattering processes controlling the shape of the one-particle spectral functions and, in some cases, of the physical response of the system. In particular, we will discuss the underlying general idea, the common threads and the specific peculiarities of all the proposed approaches. While all of them rely on a selective analysis of the Schwinger–Dyson (or the Bethe–Salpeter) equation, the methodological differences originate from the specific two-particle vertex functions to be computed and decomposed. Finally, we illustrate the potential strength of these methodologies by means of their applications the two-dimensional Hubbard model, and we provide an outlook over the future perspective and developments of this route for understanding the physics of correlated electrons.

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Nonlocal correlations and spectral properties of the Falicov-Kimball model

Cited by 50 publications

References 54 publications

Nonperturbative landscape of the Mott-Hubbard transition: Multiple divergence lines around the critical endpoint

Nonperturbative landscape of the Mott-Hubbard transition: Multiple divergence lines around the critical endpoint

Second-order dual fermion for multi-orbital systems

How to read between the lines of electronic spectra: the diagnostics of fluctuations in strongly correlated electron systems

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