Strongly correlated multi-impurity models: The crossover from a single-impurity problem to lattice models

We study, using numerical exact diagonalisation, some static and dynamical properties of a single impurity substituted into a one-dimensional repulsive Hubbard chain. A systematic scan of the parameter-space reveals a rich magnetic phase diagram. Interactions on the lattice stabilize the local moment phase of the impurity. A scalar impurity is seen to induce local moments on the neighbouring sites near Half Filling. Static spin and charge correlation functions reflect a non-Fermi liquid character of the ground state in the presence of a scalar impurity.

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Quantum Impurity Models as Reference Systems for Strongly Correlated Materials: The Road from the Kondo Impurity Model to First Principles Electronic Structure Calculations with Dynamical Mean-Field Theory

Journal of the Physical Society of Japan ◽

10.1143/jpsj.74.147 ◽

2005 ◽

Vol 74 (1) ◽

pp. 147-154 ◽

Cited By ~ 4

Author(s):

Gabriel Kotliar

Keyword(s):

First Principles ◽

Mean Field Theory ◽

Mean Field ◽

Strongly Correlated ◽

Strongly Correlated Materials ◽

The Road ◽

Impurity Model ◽

Quantum Impurity ◽

Impurity Models ◽

Structure Calculations

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Strongly Correlated Systems in Infinite Dimensions and Their Zero Dimensional Counterparts

International Journal of Modern Physics B ◽

10.1142/s0217979292000426 ◽

1992 ◽

Vol 06 (05n06) ◽

pp. 705-730 ◽

Cited By ~ 60

Author(s):

Antoine Georges ◽

Gabriel Kotliar ◽

Qimiao Si

Keyword(s):

Mean Field ◽

Strongly Correlated Systems ◽

Kondo Lattice ◽

Strongly Correlated ◽

Infinite Dimensions ◽

Field Equations ◽

Correlated Systems ◽

Infinite Dimensional ◽

Mean Field Equations ◽

Impurity Models

We extend a mapping from infinite dimensional to zero dimensional (impurity) models to derive mean field equations of several strongly correlated systems which become exact in infinite dimensions. We discuss various magnetic phases of the Hubbard model, the periodic Anderson model the Kondo lattice and the Falicov Kimball model and we relate them to different impurity models. Qualitative insights into these models is gained from the exact results obtained for their zero dimensional counterparts.

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RENORMALIZATION GROUP APPROACHES TO STRONGLY CORRELATED ELECTRON SYSTEMS

International Journal of Modern Physics B ◽

10.1142/s0217979201006367 ◽

2001 ◽

Vol 15 (19n20) ◽

pp. 2549-2567 ◽

Cited By ~ 4

Author(s):

A. C. HEWSON ◽

S. C. BRADLEY ◽

R. BULLA ◽

Y. ŌNO

Keyword(s):

Perturbation Theory ◽

Renormalization Group ◽

Magnetic Impurity ◽

Strongly Correlated Electron Systems ◽

Strongly Correlated ◽

Electron Systems ◽

Strongly Correlated Electron ◽

Correlated Electron Systems ◽

Correlated Electron ◽

Impurity Models

In recent years the numerical renormalization group (NRG) method has been extended to the calculation of dynamic response functions and transport properties of magnetic impurity models. The approach can now be applied more widely to lattice models of strongly correlated electron systems by the use of dynamical mean field theory (DMFT), in which the lattice problem is transformed into one for an effective impurity with an additional self-consistency constraint. We review these developments and assess the potential for further applications of this approach. We also discuss an alternative approach to renormalization, renormalized perturbation theory, in which the leading asymptotically exact results for the low temperature regime for a number of magnetic impurity models can be obtained within finite order perturbation theory.

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